Safe to store access token inside AsyncStorage?

AsyncStorage may not be the good solution, depend how your server handle your request.

However you can use Redux, and Redux-persist, using the transform parameter you can encrypt your data,

https://github.com/rt2zz/redux-persist#transforms

key encryption : https://github.com/maxdeviant/redux-persist-transform-encrypt

You will still use AsyncStorage, but this time with encryption layer, to protect your data

Redux is about data flow control. Not necessarily long term storage. If you want to persist redux data you will end up using AsyncStorage to do so.

AsyncStorage is sandboxed on non-jailbroken iOS devices. However, the data is not encrypted in any way.

A more secure solution for both platforms seems to be https://github.com/pradeep1991singh/react-native-secure-key-store