What do you do when a taken guy flirts with you and then says you're only his friend?

Forget him. IF he does like you and you guys go out he's already shown he will do things behind your back and they will probably progress further than holding hands.

For your question though: The reason he might be holding your hand could be because he's testing the waters. He might be trying to see what you're okay with and what he shouldn't do with you because you're uncomfortable or have a problem with it since he's taken.

Do you really want a guy that is flirtations in this way when he has a girl friend already? Cause if this is the way he is when he is in a relationship with someone, its not gonna be different with you.
This guy is what I would refer to as a Jerker. He likes to do things to test boundary and he could cares less what it does to the other person nor his girlfriend. He doesn't care about the confusion that it brings to you and he's a smooth talker.
Is this really what you want? Someone that likes jerking people around, only cares about himself and smooth talks his way out of situations?
He is a Big Capital L! You will be in a roller coaster of pain if you continue on with him.