partypoker, $0.23 + $0.02 - Hold'em No Limit - 15/30 - 2 players
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Player1 (SB): 641 (21 bb)
Hero (BB): 859 (29 bb)

Pre-Flop: (45) Hero (Hero) is BB with K♣ A♦
Player1 (SB) calls 15, Hero (BB) raises to 66, Player1 (SB) calls 36

Flop: (132) 5♠ 2♠ K♥ (2 players)
Hero (BB) bets 44, Player1 (SB) raises to 88, Hero (BB) raises to 293, Player1 (SB) raises to 575 (all-in), Hero (BB) calls 282

Turn: (1,282) Q♠ (2 players, 1 all-in)

River: (1,282) 9♠ (2 players, 1 all-in)

Total pot: 1,282

Showdown:
Player1 (SB) shows 5♣ 4♠ (a flush, Queen high)
(Equity - Pre-Flop: 38%, Flop: 24%, Turn: 32%, River: 100%)

Hero (BB) shows K♣ A♦ (a pair of Kings)
(Equity - Pre-Flop: 62%, Flop: 76%, Turn: 68%, River: 0%)

Player1 (SB) wins 1,282

it was well played you had bad luck, in a spin and go the range should be wider but this is not your case you had AK to fold with that flop would have been a mistake, well played just bad luck

Call. Sometimes you get sucked out against, but that's a part of the game

This was my thinking I had him/her on a str8 or flush draw so thought call would be the right play.

Call, in that micro game is to many donks, so call even without top kicker

Don't really think you can fold here you got sucked out on think he can have worse kings or straight or flush draws sure he can have 55 or 22 or even funky k5 k2 combos

I think that $0.25 in Spin&Go most the time is bingo game, so considering that you are in HU with AK and with a K on flop I prefer shove at flop and dont let him/her see cheap the other streets to catch some good hand like in this case he/she catched.

I don't get why you 3bet on the flop instead of shoving, you are giving them a better price to call with a draw and make your turn play harder.
Besides that well played and unlucky.

I’d also shove all in on the flop over his reraise. Just unlucky!

Stop being results oriented. Would you be posting this hand had you won the pot? Dont doubt yourself...stacking off with top top in the micros is the correct play all day everyday - you should be playing stakes you are well bank rolled for and folding a hand as strong as AK when we flop a K is just madness at these levels. You were a pretty sizable favorite on the flop, it just didnt work out for you. That is ok - take a note on the guy, move on!

Your preflop raise was to small, and you flop bet was also to small. Other than that everything is fine. You are not folding TPTK on the flop in a raised heads-up pot, when the hand start with 21BB effective. If he can beat that, or if he get there later, good for him. In this case you were ahead, when the chips went in, and then there is really not any reason to think, you should have folded.