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Why would you want to do that? Just keep on using your King account. You log in once and that's it.
The real issue is losing your inventory if you switch devices or reinstall the game.
I used to play through my Facebook account but recently created a King account in order to use this forum. I totally don't remember how it happened but my progress is now also synced with my King account. All it took was logging in once on the same device. No idea if the opposite also works. I still don't think there's an actual benefit in switching to logging in through Facebook.