This gist shows how to add support for redux-thunk and redux-promise-middleware to the flowtype libdefs for redux

redux_v3.x.x.jsx

// flow-typed signature: ba132c96664f1a05288f3eb2272a3c35
// flow-typed version: c4bbd91cfc/redux_v3.x.x/flow_>=v0.33.x

declare module 'redux' {

  /*

    S = State
    A = Action

  */

  /* NEW: We create a few extra action and dispatch types */
  declare type ThunkAction<S, R> = (dispatch: Dispatch<S, any>, getState: () => S) => R;
  declare type PromiseAction<R> = { type: string, payload: Promise<R> };
  declare type ThunkDispatch<S> = <R>(action: ThunkAction<S, R>) => R;
  declare type PromiseDispatch = <R>(action: PromiseAction<R>) => Promise<R>;
  declare type PlainDispatch<A: {type: $Subtype<string>}> = (action: A) => A;
  /* NEW: Dispatch is now a combination of these different dispatch types */
  declare type Dispatch<S, A> = PlainDispatch<A> & ThunkDispatch<S> & PromiseDispatch;

  declare type MiddlewareAPI<S, A> = {
    dispatch: Dispatch<S, A>;
    getState(): S;
  };

  declare type Store<S, A> = {
    // rewrite MiddlewareAPI members in order to get nicer error messages (intersections produce long messages)
    dispatch: Dispatch<S, A>;
    getState(): S;
    subscribe(listener: () => void): () => void;
    replaceReducer(nextReducer: Reducer<S, A>): void
  };

  declare type Reducer<S, A> = (state: S, action: A) => S;

  declare type Middleware<S, A> =
    (api: MiddlewareAPI<S, A>) =>
      (next: Dispatch<S, A>) => Dispatch<S, A>;

  declare type StoreCreator<S, A> = {
    (reducer: Reducer<S, A>, enhancer?: StoreEnhancer<S, A>): Store<S, A>;
    (reducer: Reducer<S, A>, preloadedState: S, enhancer?: StoreEnhancer<S, A>): Store<S, A>;
  };

  declare type StoreEnhancer<S, A> = (next: StoreCreator<S, A>) => StoreCreator<S, A>;

  declare function createStore<S, A>(reducer: Reducer<S, A>, enhancer?: StoreEnhancer<S, A>): Store<S, A>;
  declare function createStore<S, A>(reducer: Reducer<S, A>, preloadedState: S, enhancer?: StoreEnhancer<S, A>): Store<S, A>;

  declare function applyMiddleware<S, A>(...middlewares: Array<Middleware<S, A>>): StoreEnhancer<S, A>;

  declare type ActionCreator<A, B> = (...args: Array<B>) => A;
  declare type ActionCreators<K, A> = { [key: K]: ActionCreator<A, any> };

  declare function bindActionCreators<S, A, C: ActionCreator<A, any>>(actionCreator: C, dispatch: Dispatch<S, A>): C;
  declare function bindActionCreators<S, A, K, C: ActionCreators<K, A>>(actionCreators: C, dispatch: Dispatch<S, A>): C;

  declare function combineReducers<O: Object, A>(reducers: O): Reducer<$ObjMap<O, <S>(r: Reducer<S, any>) => S>, A>;

  declare function compose<S, A>(...fns: Array<StoreEnhancer<S, A>>): Function;

}