I'd flat here just because I don't think villain is really going to be calling turn raise and then a bet on the river with kx. I would assume he is far more likely to c/c river than b/c turn. Also if we call turn and bet river our line looks a ton more like hearts.

+ here's villains turn equity with the non set portion of his range


Hand 0: 87.226% 86.29% 00.94% 1101 12.00 { AdAh }
Hand 1: 12.774% 11.83% 00.94% 151 12.00 { AcKc, AsKs, KQs, KhJh, KhTh, AcKd, AcKh, AcKs, AsKc, AsKd, AsKh, KJo+ }

Ie. letting him draw really isn't THAT bad

just the $.02 from a guy who pays $.02 blinds