diff --git a/keyserver/flow-typed/npm/react-redux_v7.x.x.js b/keyserver/flow-typed/npm/react-redux_v7.x.x.js
--- a/keyserver/flow-typed/npm/react-redux_v7.x.x.js
+++ b/keyserver/flow-typed/npm/react-redux_v7.x.x.js
@@ -57,7 +57,7 @@
     // and provide the StateProps type to the SP type parameter.
     | ((state: S, ownProps: OP) => (state: S, ownProps: OP) => SP);
 
-  declare type Bind<D> = <A, R>((...A) => R) => (...A) => $Call<D, R>;
+  declare type Bind<D> = <A, R>((...A) => R) => (...A) => ReturnType<D>;
 
   declare type MapDispatchToPropsFn<D, OP, DP> =
     | ((dispatch: D, ownProps: OP) => DP)
@@ -91,6 +91,13 @@
   declare type MergeOPDP<OP, DP> = {| ...$Exact<OP>, ...DP |};
   declare type MergeOPSPDP<OP, SP, DP> = {| ...$Exact<OP>, ...SP, ...DP |};
 
+  declare type MapDispatch<DP, D, R> = {
+    [K in $Keys<DP>]:
+      DP[K] extends (...args: infer A) => R
+        ? (...A) => ReturnType<D>
+        : empty
+  };
+
   declare export function connect<P, OP, SP, DP, S, D>(
     mapStateToProps?: null | void,
     mapDispatchToProps?: null | void,
@@ -123,7 +130,7 @@
     mapDispatchToProps: DP,
     mergeProps?: null | void,
     options?: ?Options<S, OP, {||}, MergeOPDP<OP, DP>>,
-  ): Connector<P, OP, MergeOPDP<OP, $ObjMap<DP, Bind<D>>>>;
+  ): Connector<P, OP, MergeOPDP<OP, MapDispatch<DP, D>>>;
 
   declare export function connect<P, OP, SP, DP, S, D>(
     // If you get error here try adding return type to your mapStateToProps function
@@ -139,7 +146,7 @@
     mapDispatchToProps: DP,
     mergeProps?: null | void,
     options?: ?Options<S, OP, SP, MergeOPSPDP<OP, SP, DP>>,
-  ): Connector<P, OP, MergeOPSPDP<OP, SP, $ObjMap<DP, Bind<D>>>>;
+  ): Connector<P, OP, MergeOPSPDP<OP, SP, MapDispatch<DP, D>>>;
 
   // With `mergeProps` argument
 
@@ -180,7 +187,7 @@
   declare export function connect<P, OP, SP: {||}, DP, S, D>(
     mapStateToProps: null | void,
     mapDispatchToProps: DP,
-    mergeProps: MergeProps<P, OP, {||}, $ObjMap<DP, Bind<D>>>,
+    mergeProps: MergeProps<P, OP, {||}, {[K in keyof DP]: ReturnType<D>}>,
     options?: ?Options<S, OP, {||}, P>,
   ): Connector<P, OP, P>;
 
@@ -199,7 +206,7 @@
   declare export function connect<P, OP, SP, DP, S, D>(
     mapStateToProps: MapStateToProps<S, OP, SP>,
     mapDispatchToProps: DP,
-    mergeProps: MergeProps<P, OP, SP, $ObjMap<DP, Bind<D>>>,
+    mergeProps: MergeProps<P, OP, SP, {[K in keyof DP]: ReturnType<D>}>,
     options?: ?Options<S, OP, SP, P>,
   ): Connector<P, OP, P>;
 
diff --git a/keyserver/flow-typed/npm/redux_v4.x.x.js b/keyserver/flow-typed/npm/redux_v4.x.x.js
--- a/keyserver/flow-typed/npm/redux_v4.x.x.js
+++ b/keyserver/flow-typed/npm/redux_v4.x.x.js
@@ -97,7 +97,7 @@
   ): C;
 
   declare export function combineReducers<RootState: {...}, A>(
-    reducers: $ObjMap<RootState, <V>(V) => Reducer<V, A>>,
+    reducers: {[K in keyof RootState]: Reducer<RootState[K], A>}
   ): Reducer<RootState, A>;
 
   declare function _compose(): <T>(a: T) => T;
diff --git a/lib/flow-typed/npm/react-redux_v7.x.x.js b/lib/flow-typed/npm/react-redux_v7.x.x.js
--- a/lib/flow-typed/npm/react-redux_v7.x.x.js
+++ b/lib/flow-typed/npm/react-redux_v7.x.x.js
@@ -91,6 +91,13 @@
   declare type MergeOPDP<OP, DP> = {| ...$Exact<OP>, ...DP |};
   declare type MergeOPSPDP<OP, SP, DP> = {| ...$Exact<OP>, ...SP, ...DP |};
 
+  declare type MapDispatch<DP, D, R> = {
+    [K in $Keys<DP>]:
+      DP[K] extends (...args: infer A) => R
+        ? (...A) => ReturnType<D>
+        : empty
+  };
+
   declare export function connect<P, OP, SP, DP, S, D>(
     mapStateToProps?: null | void,
     mapDispatchToProps?: null | void,
@@ -123,7 +130,7 @@
     mapDispatchToProps: DP,
     mergeProps?: null | void,
     options?: ?Options<S, OP, {||}, MergeOPDP<OP, DP>>,
-  ): Connector<P, OP, MergeOPDP<OP, $ObjMap<DP, Bind<D>>>>;
+  ): Connector<P, OP, MergeOPDP<OP, MapDispatch<DP, D>>>;
 
   declare export function connect<P, OP, SP, DP, S, D>(
     // If you get error here try adding return type to your mapStateToProps function
@@ -139,7 +146,7 @@
     mapDispatchToProps: DP,
     mergeProps?: null | void,
     options?: ?Options<S, OP, SP, MergeOPSPDP<OP, SP, DP>>,
-  ): Connector<P, OP, MergeOPSPDP<OP, SP, $ObjMap<DP, Bind<D>>>>;
+  ): Connector<P, OP, MergeOPSPDP<OP, SP, MapDispatch<DP, D>>>;
 
   // With `mergeProps` argument
 
@@ -180,7 +187,7 @@
   declare export function connect<P, OP, SP: {||}, DP, S, D>(
     mapStateToProps: null | void,
     mapDispatchToProps: DP,
-    mergeProps: MergeProps<P, OP, {||}, $ObjMap<DP, Bind<D>>>,
+    mergeProps: MergeProps<P, OP, {||}, {[K in keyof DP]: ReturnType<D>}>,
     options?: ?Options<S, OP, {||}, P>,
   ): Connector<P, OP, P>;
 
@@ -199,7 +206,7 @@
   declare export function connect<P, OP, SP, DP, S, D>(
     mapStateToProps: MapStateToProps<S, OP, SP>,
     mapDispatchToProps: DP,
-    mergeProps: MergeProps<P, OP, SP, $ObjMap<DP, Bind<D>>>,
+    mergeProps: MergeProps<P, OP, SP, {[K in keyof DP]: ReturnType<D>}>,
     options?: ?Options<S, OP, SP, P>,
   ): Connector<P, OP, P>;
 
diff --git a/lib/flow-typed/npm/redux_v4.x.x.js b/lib/flow-typed/npm/redux_v4.x.x.js
--- a/lib/flow-typed/npm/redux_v4.x.x.js
+++ b/lib/flow-typed/npm/redux_v4.x.x.js
@@ -97,7 +97,7 @@
   ): C;
 
   declare export function combineReducers<RootState: {...}, A>(
-    reducers: $ObjMap<RootState, <V>(V) => Reducer<V, A>>,
+    reducers: {[K in keyof RootState]: Reducer<RootState[K], A>}
   ): Reducer<RootState, A>;
 
   declare function _compose(): <T>(a: T) => T;
diff --git a/lib/flow-typed/npm/reselect_v3.x.x.js b/lib/flow-typed/npm/reselect_v3.x.x.js
--- a/lib/flow-typed/npm/reselect_v3.x.x.js
+++ b/lib/flow-typed/npm/reselect_v3.x.x.js
@@ -888,7 +888,7 @@
     createStructuredSelector: <TState, TProps, InputSelectors: {[k: string | number]: InputSelector<TState, TProps, any>}>(
       inputSelectors: InputSelectors,
       selectorCreator?: SelectorCreator
-    ) => OutputSelector<TState, TProps, $ObjMap<InputSelectors, ExtractReturnType>>
+    ) => OutputSelector<TState, TProps, {[K in keyof InputSelectors]: ReturnType<InputSelectors[K]>}>
   };
 
   declare module.exports: Reselect;
diff --git a/lib/flow-typed/npm/tcomb_v3.x.x.js b/lib/flow-typed/npm/tcomb_v3.x.x.js
--- a/lib/flow-typed/npm/tcomb_v3.x.x.js
+++ b/lib/flow-typed/npm/tcomb_v3.x.x.js
@@ -86,7 +86,7 @@
 
   declare type TypeToValidator = <V>(v: V) => TType<V>;
 
-  declare export type TStructProps<+T> = $ObjMap<T, TypeToValidator>;
+  declare export type TStructProps<+T> = {[K in keyof T]: TType<T[K]>};
   declare type TStructOptions = {
     name?: string,
     strict?: boolean,
diff --git a/lib/shared/identity-client-context.js b/lib/shared/identity-client-context.js
--- a/lib/shared/identity-client-context.js
+++ b/lib/shared/identity-client-context.js
@@ -12,11 +12,9 @@
 
 export type PartialAuthMetadata = Partial<AuthMetadata>;
 
-// TODO: Replace this with mapped type after Flow upgrade
-export type FullAuthMetadata = $ObjMap<
-  AuthMetadata,
-  <T>(prop: T) => $NonMaybeType<T>,
->;
+export type FullAuthMetadata = {
+  [K in keyof AuthMetadata]: $NonMaybeType<AuthMetadata[K]>,
+};
 
 export type IdentityClientContextType = {
   +identityClient: IdentityServiceClient,
diff --git a/lib/socket/inflight-requests.js b/lib/socket/inflight-requests.js
--- a/lib/socket/inflight-requests.js
+++ b/lib/socket/inflight-requests.js
@@ -32,10 +32,11 @@
   reject: (error: Error) => void,
   messageID: number,
 };
-type InflightRequestMap = $ObjMap<
-  ValidResponseMessageMap,
-  <T>(T) => BaseInflightRequest<$Exact<T>>,
->;
+type InflightRequestMap = {
+  [K in keyof ValidResponseMessageMap]: BaseInflightRequest<
+    $Exact<ValidResponseMessageMap[K]>,
+  >,
+};
 
 type ValidResponseMessage = $Values<ValidResponseMessageMap>;
 type InflightRequest = $Values<InflightRequestMap>;
diff --git a/lib/types/subscription-types.js b/lib/types/subscription-types.js
--- a/lib/types/subscription-types.js
+++ b/lib/types/subscription-types.js
@@ -10,10 +10,10 @@
   pushNotifs: 'pushNotifs',
 });
 
-export type ThreadSubscription = $ObjMap<
-  typeof threadSubscriptions,
-  () => boolean,
->;
+export type ThreadSubscription = {
+  // eslint-disable-next-line no-unused-vars
+  [K in keyof typeof threadSubscriptions]: boolean,
+};
 
 export const threadSubscriptionValidator: TInterface<ThreadSubscription> =
   tShape<ThreadSubscription>(_mapValues(() => t.Boolean)(threadSubscriptions));
diff --git a/lib/utils/promises.js b/lib/utils/promises.js
--- a/lib/utils/promises.js
+++ b/lib/utils/promises.js
@@ -3,10 +3,13 @@
 import sleep from './sleep.js';
 
 type Promisable<T> = Promise<T> | T;
+type PromiseAllResult<T> = {
+  [K in keyof T]: T[K] extends Promisable<infer U> ? U : T[K],
+};
 
 async function promiseAll<T: { +[key: string]: Promisable<mixed> }>(
   input: T,
-): Promise<$ObjMap<T, typeof $await>> {
+): Promise<PromiseAllResult<T>> {
   const promises = [];
   const keys = Object.keys(input);
   for (let i = 0; i < keys.length; i++) {
@@ -15,7 +18,7 @@
     promises.push(promise);
   }
   const results = await Promise.all(promises);
-  const byName: { [string]: mixed } = {};
+  const byName: PromiseAllResult<T> = { ...input };
   for (let i = 0; i < keys.length; i++) {
     const key = keys[i];
     byName[key] = results[i];
diff --git a/native/flow-typed/npm/@react-navigation/core_v6.x.x.js b/native/flow-typed/npm/@react-navigation/core_v6.x.x.js
--- a/native/flow-typed/npm/@react-navigation/core_v6.x.x.js
+++ b/native/flow-typed/npm/@react-navigation/core_v6.x.x.js
@@ -952,10 +952,7 @@
   declare export type ScreenListeners<
     State: NavigationState = NavigationState,
     EventMap: EventMapBase = EventMapCore<State>,
-  > = $ObjMapi<
-    {| [name: $Keys<EventMap>]: empty |},
-    <K: $Keys<EventMap>>(K, empty) => EventListenerCallback<K, State, EventMap>,
-  >;
+  > = {[K in $Keys<EventMap>]: EventListenerCallback<K, State, EventMap>};
   declare type ScreenListenersProp<
     ScreenListenersParam: {...},
     RouteParam,
diff --git a/native/flow-typed/npm/react-native-reanimated_v2.x.x.js b/native/flow-typed/npm/react-native-reanimated_v2.x.x.js
--- a/native/flow-typed/npm/react-native-reanimated_v2.x.x.js
+++ b/native/flow-typed/npm/react-native-reanimated_v2.x.x.js
@@ -519,7 +519,7 @@
   declare type ToValue = (val: mixed) => ValueImpl;
   declare type Event = <T: { ... }, E: $Event<T> = $Event<T>>(
     defs: $ReadOnlyArray<{
-      +nativeEvent: Partial<$ObjMap<E, ToValue>>,
+      +nativeEvent: Partial<{[K in keyof E]: ValueImpl}>,
       ...
     }>,
   ) => EventResult<T, E>;
diff --git a/native/flow-typed/npm/react-redux_v7.x.x.js b/native/flow-typed/npm/react-redux_v7.x.x.js
--- a/native/flow-typed/npm/react-redux_v7.x.x.js
+++ b/native/flow-typed/npm/react-redux_v7.x.x.js
@@ -91,6 +91,13 @@
   declare type MergeOPDP<OP, DP> = {| ...$Exact<OP>, ...DP |};
   declare type MergeOPSPDP<OP, SP, DP> = {| ...$Exact<OP>, ...SP, ...DP |};
 
+  declare type MapDispatch<DP, D, R> = {
+    [K in $Keys<DP>]:
+      DP[K] extends (...args: infer A) => R
+        ? (...A) => ReturnType<D>
+        : empty
+  };
+
   declare export function connect<P, OP, SP, DP, S, D>(
     mapStateToProps?: null | void,
     mapDispatchToProps?: null | void,
@@ -123,7 +130,7 @@
     mapDispatchToProps: DP,
     mergeProps?: null | void,
     options?: ?Options<S, OP, {||}, MergeOPDP<OP, DP>>,
-  ): Connector<P, OP, MergeOPDP<OP, $ObjMap<DP, Bind<D>>>>;
+  ): Connector<P, OP, MergeOPDP<OP,MapDispatch<DP, D>>>;
 
   declare export function connect<P, OP, SP, DP, S, D>(
     // If you get error here try adding return type to your mapStateToProps function
@@ -139,7 +146,7 @@
     mapDispatchToProps: DP,
     mergeProps?: null | void,
     options?: ?Options<S, OP, SP, MergeOPSPDP<OP, SP, DP>>,
-  ): Connector<P, OP, MergeOPSPDP<OP, SP, $ObjMap<DP, Bind<D>>>>;
+  ): Connector<P, OP, MergeOPSPDP<OP, SP, MapDispatch<DP, D>>>;
 
   // With `mergeProps` argument
 
@@ -180,7 +187,7 @@
   declare export function connect<P, OP, SP: {||}, DP, S, D>(
     mapStateToProps: null | void,
     mapDispatchToProps: DP,
-    mergeProps: MergeProps<P, OP, {||}, $ObjMap<DP, Bind<D>>>,
+    mergeProps: MergeProps<P, OP, {||}, {[K in keyof DP]: ReturnType<D>}>,
     options?: ?Options<S, OP, {||}, P>,
   ): Connector<P, OP, P>;
 
@@ -199,7 +206,7 @@
   declare export function connect<P, OP, SP, DP, S, D>(
     mapStateToProps: MapStateToProps<S, OP, SP>,
     mapDispatchToProps: DP,
-    mergeProps: MergeProps<P, OP, SP, $ObjMap<DP, Bind<D>>>,
+    mergeProps: MergeProps<P, OP, SP, {[K in keyof DP]: ReturnType<D>}>,
     options?: ?Options<S, OP, SP, P>,
   ): Connector<P, OP, P>;
 
diff --git a/native/flow-typed/npm/reselect_v3.x.x.js b/native/flow-typed/npm/reselect_v3.x.x.js
--- a/native/flow-typed/npm/reselect_v3.x.x.js
+++ b/native/flow-typed/npm/reselect_v3.x.x.js
@@ -888,7 +888,7 @@
     createStructuredSelector: <TState, TProps, InputSelectors: {[k: string | number]: InputSelector<TState, TProps, any>}>(
       inputSelectors: InputSelectors,
       selectorCreator?: SelectorCreator
-    ) => OutputSelector<TState, TProps, $ObjMap<InputSelectors, ExtractReturnType>>
+    ) => OutputSelector<TState, TProps, {[K in keyof InputSelectors]: ReturnType<InputSelectors[K]>}>
   };
 
   declare module.exports: Reselect;
diff --git a/native/themes/colors.js b/native/themes/colors.js
--- a/native/themes/colors.js
+++ b/native/themes/colors.js
@@ -286,8 +286,7 @@
 
 type Styles = { [name: string]: { [field: string]: mixed } };
 
-type ReplaceField = (input: any) => any;
-export type StyleSheetOf<S: Styles> = $ReadOnly<$ObjMap<S, ReplaceField>>;
+export type StyleSheetOf<S: Styles> = $ReadOnly<{ [$Keys<S>]: any }>;
 
 function stylesFromColors<IS: Styles>(
   obj: IS,
diff --git a/web/flow-typed/npm/react-redux_v7.x.x.js b/web/flow-typed/npm/react-redux_v7.x.x.js
--- a/web/flow-typed/npm/react-redux_v7.x.x.js
+++ b/web/flow-typed/npm/react-redux_v7.x.x.js
@@ -90,6 +90,13 @@
   declare type MergeOPSP<OP, SP, D> = {| ...$Exact<OP>, ...SP, dispatch: D |};
   declare type MergeOPDP<OP, DP> = {| ...$Exact<OP>, ...DP |};
   declare type MergeOPSPDP<OP, SP, DP> = {| ...$Exact<OP>, ...SP, ...DP |};
+  
+  declare type MapDispatch<DP, D, R> = {
+    [K in $Keys<DP>]:
+      DP[K] extends (...args: infer A) => R
+        ? (...A) => ReturnType<D>
+        : empty
+  };
 
   declare export function connect<P, OP, SP, DP, S, D>(
     mapStateToProps?: null | void,
@@ -123,7 +130,7 @@
     mapDispatchToProps: DP,
     mergeProps?: null | void,
     options?: ?Options<S, OP, {||}, MergeOPDP<OP, DP>>,
-  ): Connector<P, OP, MergeOPDP<OP, $ObjMap<DP, Bind<D>>>>;
+  ): Connector<P, OP, MergeOPDP<OP, MapDispatch<DP, D>>>;
 
   declare export function connect<P, OP, SP, DP, S, D>(
     // If you get error here try adding return type to your mapStateToProps function
@@ -139,7 +146,7 @@
     mapDispatchToProps: DP,
     mergeProps?: null | void,
     options?: ?Options<S, OP, SP, MergeOPSPDP<OP, SP, DP>>,
-  ): Connector<P, OP, MergeOPSPDP<OP, SP, $ObjMap<DP, Bind<D>>>>;
+  ): Connector<P, OP, MergeOPSPDP<OP, SP, MapDispatch<DP, D>>>;
 
   // With `mergeProps` argument
 
@@ -180,7 +187,7 @@
   declare export function connect<P, OP, SP: {||}, DP, S, D>(
     mapStateToProps: null | void,
     mapDispatchToProps: DP,
-    mergeProps: MergeProps<P, OP, {||}, $ObjMap<DP, Bind<D>>>,
+    mergeProps: MergeProps<P, OP, {||}, {[K in keyof DP]: ReturnType<D>}>,
     options?: ?Options<S, OP, {||}, P>,
   ): Connector<P, OP, P>;
 
@@ -199,7 +206,7 @@
   declare export function connect<P, OP, SP, DP, S, D>(
     mapStateToProps: MapStateToProps<S, OP, SP>,
     mapDispatchToProps: DP,
-    mergeProps: MergeProps<P, OP, SP, $ObjMap<DP, Bind<D>>>,
+    mergeProps: MergeProps<P, OP, SP, {[K in keyof DP]: ReturnType<D>}>,
     options?: ?Options<S, OP, SP, P>,
   ): Connector<P, OP, P>;
 
diff --git a/web/flow-typed/npm/reselect_v3.x.x.js b/web/flow-typed/npm/reselect_v3.x.x.js
--- a/web/flow-typed/npm/reselect_v3.x.x.js
+++ b/web/flow-typed/npm/reselect_v3.x.x.js
@@ -888,7 +888,7 @@
     createStructuredSelector: <TState, TProps, InputSelectors: {[k: string | number]: InputSelector<TState, TProps, any>}>(
       inputSelectors: InputSelectors,
       selectorCreator?: SelectorCreator
-    ) => OutputSelector<TState, TProps, $ObjMap<InputSelectors, ExtractReturnType>>
+    ) => OutputSelector<TState, TProps, {[K in keyof InputSelectors]: ReturnType<InputSelectors[K]>}>
   };
 
   declare module.exports: Reselect;