$2 NLHE 6-max: SB vs BTN 3bet OOP overpair on very wet board flop decision

888Poker Snap, Hold'em No Limit - $0.01/$0.02 - 6 players
Hand delivered by Upswing Poker

UTG: $0.62 (31 bb)
MP: $3.94 (197 bb)
CO: $2.80 (140 bb)
BU: $2.24 (112 bb)
SB (Hero): $1.88 (94 bb)
BB: $1.12 (56 bb)

Pre-Flop: ($0.03) Hero is SB with K♦ K♥
3 players fold, BTN raises to $0.08, Hero 3-bets to $0.25, 1 fold, BTN calls $0.17

Flop: ($0.52) 9♣ 8♠ T♠ (2 players)

How would you approach this hand generally?
Is check/call flop standard then check/fold turn for any bad cards like spade,7,J,Q,A. Villain is an unknown.

I don't think it's ever a good idea to check/call with KK on this flop. You have an overpair so you want to start extracting value from flush and straight draws that may be in your villain's range. I think you'd Cbet for value here and expecting villain to probably jam with worse cards.

3B bigger oop as default.

The flop spr is close to 3. Gii unless you have an extreme read villain has you beat.

Bet flop small .33-.45 psb. Jam to any raise.

Yeah an awful flop for kk but id still be cbetting here with the intention of getting it in on the flop if you face a raise, even though this would be a high variance situation.
Check calling is not the worst play either, this kind of turns your hand face up but players at nl2 probably aren't even aware of that.
If you check call flop I'd also be looking to check/call turn on most bet sizes even if a bad card does come for us with the intention of folding on the river. Check folding turn is a little too nitty.

-Your 3bet size is too small. You are offering very good pot odds for villain, especially OOP. 3bet bigger like $0,30.
- Given that villain is unknown, you can make a bet like 1/2 psb or a little more. You can give him a good price to call with his possible draws. Your 3bet size invites him to call preflop with a wider range, including speculative hands.