Heads up I 3 bet that flop, if he caps I probably fold the turn if another diamond hits.
If the turn is not a diamond and he leads out I probably call down.
Since you just called the flop I too would bet the turn and then take the free showdown.
If he was incredibly passive normally I'd fold to his turn bet (after a cap) if it wasn't a diamond, but he'd have to be quite passive.
KK and AA I play exactly the same way, they're overpairs and I think I'm ahead right now.

Also you're not going to push him off a flush heads up probably, so my turn bet is more for value or to get him to fold another pair, because he's pretty much telling me he doesn't have a flush

True, you normally don't want to push out bluffs, but we need to know what our opponent has. You really shouldn't c/c all the way down with an overpair into a 4 flush board, you will not win that enough for that play to show a profit. You need to give the best hands the chance to fold. Its likely that the SLAG limped in with a 67s or which flopped the flush. He might even have a hand like 44 with the 4 of diamonds. Now that the board is showing 4 to a flush, how easy is it for the SLAG to call a raise with nothing more then a bad kicker. Raise, put pressure on him to drop the better hand.

4 flush, I thought we were talking about a 3 flush board, so we are assuming the tunr comes another flush card? Raising the turn for information is expensive, I dont like that option. Id rather go to showdown if that was the case. This limit poker, there is a scary board. A worse hands not calling a raise enough and better hands are not folding. A raise has no equity. After eliminating raise and folding I still believe the best option is calling. Particularly against an aggressive player. People get beat into the concept of aggression aggression aggression. In LHE sometimes not best to fight fire with fire. Give them some rope and let them hang theirself. Personally I love the line of call-call-raise the river in a lot of situations against aggressive/bluff opposition. Ive even had players look me without a pair on the river raise.