First, let's note the difference in philosophy: TypeScript aims for fast analysis because you can to compile it down to JS before you can run/test it. flowtype is meant to be an async analysis that can run continuously with changes since the last analysis, or in parallel with your eslint and bundler rules. As such, flowtype's type system and analysis is not quite as concerned with speed or memory usage in service of potentially finding more bugs.
On two occasions I have tried to roll out flow in React Native applications, and on those two occasions we ended up backing out after a few weeks. Some detail: flow doesn't have a public roadmap, and what version you use is dictated by the react/react-native dependency and the annotations in react-native itself. flowtype also has some hard-coded aspects to help the analysis for React, so major updates to React itself sometimes also require updating flowtype to match. React Native upgrades then get gated based on your dependent libraries (or flow-typed) being updated