deepstacks 10plo, how to play the nuts?

Coinpoker 10 plo
Preflop is a 3bet? or a fold or a call?
Flop we going to check/call?
Turn and river ok?
Or is it better to check/raise at 1 point to get more money in vs flushes?

Hand converted by PokerTracker 4

Hero (SB): 236.7 BB
BB: 107.6 BB (VPIP: 50.00, PFR: 25.00, 3Bet Preflop: 0.00, Hands: 8)
CO: 100 BB (VPIP: 14.29, PFR: 9.52, 3Bet Preflop: 3.45, Hands: 66)
BTN: 230.7 BB (VPIP: 21.21, PFR: 13.64, 3Bet Preflop: 3.57, Hands: 68)

4 players post ante of 0.1 BB, Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.9 BB) Hero has A♠ 6♠ K♦ 6♦

fold, BTN raises to 3.5 BB, Hero raises to 11.5 BB, fold, BTN calls 8 BB

Flop: (24.4 BB, 2 players) T♠ 9♠ 8♦
Hero checks, BTN checks

Turn: (24.4 BB, 2 players) 3♠
Hero bets 12.7 BB, BTN calls 12.7 BB

River: (49.8 BB, 2 players) 5♣
Hero bets 47.3 BB, BTN calls 47.3 BB