Hello, I have a question about betting 3 streets with TPTK with this board. Should I check behind on the turn ?

888 Poker - $0.02 NL - Holdem - 8 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

MP: 55.5 BB (VPIP: 10.67, PFR: 10.67, 3Bet Preflop: 0.00, Hands: 76)
MP+1: 160 BB (VPIP: 13.79, PFR: 1.04, 3Bet Preflop: 0.22, Hands: 1,257)
CO: 106.5 BB (VPIP: 13.30, PFR: 6.91, 3Bet Preflop: 1.61, Hands: 188)
BTN: 109.5 BB (VPIP: 11.76, PFR: 9.69, 3Bet Preflop: 7.35, Hands: 430)
Hero (SB): 177.5 BB
BB: 146.5 BB (VPIP: 22.94, PFR: 7.34, 3Bet Preflop: 0.00, Hands: 109)
UTG: 119.5 BB (VPIP: 25.50, PFR: 20.13, 3Bet Preflop: 4.00, Hands: 149)
UTG+1: 101.5 BB (VPIP: 56.47, PFR: 18.43, 3Bet Preflop: 6.25, Hands: 257)

Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has Kd Ah
fold, UTG+1 raises to 2 BB, fold, MP+1 calls 2 BB, fold, BTN calls 2 BB, Hero raises to 6 BB, fold, UTG+1 calls 4 BB, MP+1 calls 4 BB, fold

Flop : (21 BB, 3 players) 7c 9s Kc
Hero bets 13.5 BB, UTG+1 calls 13.5 BB, fold

Turn : (48 BB, 2 players) 9c
Hero bets 36 BB, UTG+1 calls 36 BB

River : (120 BB, 2 players) 3h
Hero bets 46 BB, UTG+1 calls 46 BB and is all-in

Hero shows Kd Ah (Two Pair, Kings and Nines)
(Pre 60%, Flop 53%, Turn 9%)

UTG+1 shows Qc Jc (Flush, King High)
(Pre 40%, Flop 47%, Turn 91%)

UTG+1 wins 199 BB

Yes, check the turn in this situation. You're getting the villain to play correctly: he'll call with the flush or a draw and fold with air. By checking you get to see what he does and allow him to bluff.

As played on the turn, certainly check the river -- villain just made a big call on a scary board.

Finally, in future posts, please stop your action where you would like advice -- on the turn in this case. Seeing the results of the hand will influence your advice.