Oh man that's an unlucky board for your K's. That's exactly how I would have played that hand. At the river, I think it's pretty clear that the villain didn't hit a flush draw if he was on it, and on the flop and turn you were betting good amounts so he wasn't drawing cheap. I would have doubted that he was on a straight draw.

Only thing I might have done differently is maybe bet a little higher on the turn? Maybe 80% of the pot? I'm not sure if that would be the proper play, but in that situation, I feel like that's what I would have done out of my gut feeling.