I don't mind the call on the flop at all (he'll barrel the turn a lot OOP if you just call, I think), but you have to raise turn, imo.
He's going to c/f a lot of rivers, I think. He won't bluff any missed FDs since you look like you are strong, and he may not pay off with a king for the same reason either.
You both have plenty behind, so go for stacks if he hits a flush on the river (he played it like a possible FD) or something.
This could look bluffy and he could call here with Kx hands (especially Kx of spades, of course) and it's got to be good for metagame/your overall image vs. villain and rest of table, whereas the line of b/c flop, call turn on that board looks like you're strong.
I think for this specific hand, we likely need more info like dynamics between you two and more stats/reads.
Also, I suggest using the Poker Strategy and Skills Board
in the future. I certainly hope there are more.