Bet. His hand stinks like AK with the K of clubs. If he does have a flush then you pay only 2 bets to see a showdown. If he doesn't have a flush then he'll probably check behind you and you'll miss a bet.

Seeing how its HU, he could have a wide range of hands but its unlikely he'll bet/raise with 2 pair/set on such a scary board. As such, I don't see three betting an option and check calling is just too weak of a play with the circumstances.