There are currently only the two options:

1. Use Facebook as sign in on any machine with app or browser version of game.

2. Use the app linked to the mobile machine it is launched on.

So there is no other ways, not email or anything like that.

Since you have already a team on FB there is no way to link your FB to your phone team. But, if you want to "start over" with that team, you could use the take over on a level 1 team.