Do you really need Flux with your React application? Not really. You can create very complex apps with only React and you will be fine.
Flux, Redux, MobX add better state management capability to your app. I have used Redux and the idea is to have a central data store or a single source of truth for your app. Rather than having data being defined everywhere or using web storage to save data, Redux enables you to maintain your data at a single location and then play around with it.