AK in 4bet pot

He shouldn't have many flushes here if any. Since Ad is on the board I don't see him calling preflop with something else that could have the flush. He may have AQs in some other suit, or hands like QQ, JJ. That being said I'm not sure what is the optimal strategy to get most value. I would bet 1/3 flop, 1/2 turn, check/call the river. By checking OTR you're giving him an oportunity to bluff the flushy river. If it's a weaker player he won't realise that his range doesn't have any in this spot.

1. Don't 4bet pre. If he jams you are dead meat preflop. Also, AK doesn't really have value vs his 3bet range since he is rarely 3betting hands like AQ/AJ. Call the 3bet instead.

2. Probably bet this flop most of the time. The occasional check to protect your KK/AXs/QQ is reasonable.

3. He probably has VERY few flushes and straights so you should definitely value bet twice. I don't like check/call because he mostly bets stronger hands and checks back all weaker hands, which means u pay him off when you are behind and give him a free showdown when he's behind.