An often overlooked pattern in React is controller-views. When using Flux (or really, with any external-to-the-component data) you should put this Store logic in the nearest parent to the components who use it. This component is the "controller" which gets the data and passes it as properties to the child components (who pass it as required to their children down the hierarchy).
This keeps your child components pure (fast, renders directly from props, uses PureRenderMixin) and keeps data access centralised to the nearest common controller-view component. It's okay to have a parent component that simply collects data to pass directly into a single child within the render() call — the parent fetches data and sets props, the child re-renders only when the props update, and there's a clear separation of responsibility between the two.
This keeps your child components pure (fast, renders directly from props, uses PureRenderMixin) and keeps data access centralised to the nearest common controller-view component. It's okay to have a parent component that simply collects data to pass directly into a single child within the render() call — the parent fetches data and sets props, the child re-renders only when the props update, and there's a clear separation of responsibility between the two.