therealsujitk currently when you login with Facebook or GitHub, only the email is used to match accounts. True social connect between accounts is not implemented at this time.
The current system uses the third-party oauth only to perform the login but no token is actually saved into Flarum. Flarum has no way to tell which third-party service was used for login by a user.
Only Twitter currently saves the Twitter ID on the users
table. And it's indeed lacking a disconnect button.
I think we have plans to improve the social connect experience in core, but it's probably not for the immediate future.
I think a more advanced social connect system only makes sense if the oauth token is actually needed for something, like posting on the user's Facebook page on their behalf for example. To my knowledge there has been no talk of any kind of user integration with Facebook, Twitter or GitHub until now.
In the meantime, third-party extensions can provide the missing experience. You could make an improved version of the Facebook extension that saves the oauth token, and add controls to disconnect it.