Just a bit of a necro bump (unfortunately but I'd rather keep all this in once place for things like people googling around)
Fitbit recently changed their ToS making it so my last blogpost about OAuth2 and Unity no longer viable (no longer allowed to use Webview based solutions for matters of security.)
Soooo..I spent a bunch of time googling around trying to find a solution and came across some and made another blogpost about it as well as a video tutorial.
http://technicalartistry.blogspot.ca/2016/01/fitbit-unity-oauth-2-and-native.html
Please don't be mad at my bumping, I still get a ton of people from this thread reading the posts so it's obviously still worth it to keep it in this thread :)