Having used both Flux and Redux for fairly large projects for the past two years, I have finally come to the conclusion that I really don't need either. I tried to summarize my alternative here, although I'm sure many will disagree:
I have been using React Native for a year now on a large project and came to the same conclusion. I find using Redux can quickly lead to over-engineered software.
As goes with every extra dependency: don't use it until you actually need it.
It's worked out really well for a large dashboard I'm working on. Compared to what we had before which was a mess of duplicated API calls in views with the same error handling code copy pasta'ed everywhere, with all different flavors of state management. It's not perfect (like the explosion of constants), but is probably 10x easier to maintain than what we had before.
I will say that using it by itself is probably going to be challenging. You'll want to use a connector library (like react-redux in this case), invest in some good API middleware, etc.
I hate to pile on, but we introduced react and redux at my startup and it (the project, not the company) largely failed due to the increased complexity of redux itself, and a coding style of hyper abstraction.
Maybe it works on large teams and code bases, but it is unnecessary on smaller teams where sane code practices are enough.
I wish "Redux" would go away. It's the worst thing about the React ecosystem. I use quotes because it's not even much of a library. It's like 100 lines that no one needs because the abstraction they provide is leaky to the max (e.g. no support for nested denormalied data). And it comes with pages and pages of documentation that says little or even nothing while tricking newcomers into thinking they're learning something about a useful tool.
It's remarkable to me that real clients like Relay haven't caught on as much while Redux wastes so many peoples' time.
http://zen.lk/2017/05/08/you-might-not-need-redux/