My doubt here is about the Turn, the K gives a flush possibility, the pot is too high. Should I bet one more time? If so, would it be bet/fold or bet/call?

PokerStars - $0.02 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 131.5 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 4)
SB: 111.5 BB (VPIP: 25.00, PFR: 25.00, 3Bet Preflop: -, Hands: 4)
Hero (BB): 117 BB
UTG: 111.5 BB (VPIP: 27.27, PFR: 27.27, 3Bet Preflop: 0.00, Hands: 13)
MP: 214.5 BB (VPIP: 100.00, PFR: 0.00, 3Bet Preflop: -, Hands: 1)
CO: 106.5 BB (VPIP: 25.00, PFR: 25.00, 3Bet Preflop: 0.00, Hands: 4)

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has A A

UTG raises to 3 BB, fold, fold, fold, SB calls 2.5 BB, Hero raises to 15 BB, UTG calls 12 BB, SB calls 12 BB

Flop: (45 BB, 3 players) 4 7 5
SB checks, Hero bets 28.5 BB, UTG calls 28.5 BB, fold

Turn: (102 BB, 2 players) K
Hero checks, UTG checks

River: (102 BB, 2 players) 8
Hero checks, UTG checks

Your preflop raise is reaaaally huge. I think you're going to drive out a lot of worse hands by raising more than 3x.

Even though the flush hits, you need to bet the turn. I'd opt for a small bet, you save money if he raises you and you put single diamond hands in an annoying spot.

After the turn checks through, bet! It doesn't have to be huge, but you may convince AK or KQ to make a crying call with a 1/3-1/2 pot bet. If he calls with the flush you saved money, because if he bets this small with a flush you need to call anyway (and if he lets turn check through with it that's just terrible for him).

As said pre is huge.

I can understand how you will get hesitant on this board. It's scary looking by the turn but think by going c/c on turn and river you miss value and let more draws in for nothing.

I'd probably fire turn and if called check back the river and re-evaluate. I think there needs to be some sort of pot control here looking at the board.