He is going to have a fairly substantial range advantage here. He has AA, AK where you should not.

I don't mind your line honestly. I think you can consider betting turn here and checking back rivers. Hard to get three streets when he will likely check/call down with all his AK combos. Also hard to get called by AJ for three streets unless he has the Js.

However, with his range vs range advantage, I like checking back flop here best since it is so hard to get 3 streets. Turn it in to a two street game. You are really only confident here when you spike the Ks, all other spades can be problematic. You also have a nice blocker to the flush completing when he has KsKx here and you can squeeze out a little bit of value on safe turns (like the one above) and rivers.

I think that line is fine. There definitely some other lines that hand can take with some benefits and drawbacks. Are we often bluffing the flop?

I'm fine with this line, as well as checking flop. However, with the flush draw available, I like checking flop a bit more because you aren't really afraid of any turns.

Two streets of value seems good. He can have something like KK-JJ, or even something like a A5s, which would pay off two streets.