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In the game app if you go to the settings and disconnect from Facebook then restart your phone and open the game again, you should be back at level 0. If you want to save the game then, just create a Kingdom account (the little orange crown icon) and it works in the same way as Facebook to save the game.
If you were previously connected to Facebook and want to remain so, you cannot start it again unless you start a new Facebook account and link it to that. Otherwise as the op said. A strong disadvantage of just connecting to the king site and not Facebook, lives do not come through quick enough, or as many as you would get on FB with plenty of friends.