The raise pre-flop makes a certain amount of sense. The pot size does justify calling the single bet on the flop, because you're getting huge 20:1 odds, so you're getting the right odds for the Kings full draw, which probably would be the best hand. The flush draw isn't really something that you're wanting to draw to, since it wouldn't be that strong, but you're calling anyway because of the better draw you have available.
When the Ace hits, then you know you have a flush. The higher flush is a worry, but with the paired board I think the possibility of being against a full house is as much of a worry. I'd be inclined to check or call the turn and river unless there was a raise (when I'd fold) or I hit a King (at which point I'd push some more chips in), so apart from the raise on the river I'd agree with the play.
My thinking for the checking on the river is not that they've missed their hand, necessarily - they could easily have the nut flush, but be worried about a full house being slow-played against them, which would also explain the river check. That said, if you thought there was even a moderate chance they would fold, then it could be a +ve expectation bet, because you'd risk $0.50 to try to win the pot, and it may be possible to push the nut flush off their hand if they do think you've made your full house.