he can indeed use both, and would only take one damage. In essence it would go like this:

1)Belkar flips the first rage, gains +3 on attack or defence, and this rage is supported by the second copy, so he does not take a wound at the end of the turn.
2)Belkar then flips the second rage, gains another +3 on attack or defence and as he has no additional schticks to support this one, he takes the wound at the end of the turn.

(ooooh, colours )