Blog post about integrating Facebook SDK with react-native here
Check out the example gif below (sorry it's a bit heavy) to see it in action. Note that it is in the simulator so it uses the browser for Facebook auth; it will use the Facebook app if it is available. Video background is implemented in RCTVideoPlayer RCTVideoPlayerManager VideoContentModes VideoResizeMode VideoStylePropTypes and RCTVideoPlayer.ios.js.
Feel free to use the token and user id above to get my basic information on Facebook :p
background.mp4 does not belong to me, I borrowed it from airbnb.com