nl100, KK IP 3bet pot, broadway flop

[BigDan9]

I'd check and take the free card - like you say, that flop stinks and you seem to have a good read on your oppo. A 9 might be good for you too of course (although I wouldn't get too excited) and, just possibly, one of the two remaining Ks.

Otherwise, though, I think you could peel one off if Villain doesn't make it too expensive on the turn and then either fold to another bet on the river or hope for a free showdown.