Preflop
With stacks this deep you can open a bit larger like 3BB, but 2,5BB is also fine. Facing the 3-bet its kind of close. I would definitely fold AJo, but AJs seem like an ok call.
Flop
Dont see any reason to do anything other than check-call. If you check-raise, you reopen the betting for him and might end up getting it in pretty bad against
hands like AK or KQs.
Turn
You made the flush, and I think, there are merits to leading out here to not allow him to check back. It also sets it up, so you can easily jam the river. Yes its kind of obvious, but if he overfold to this line, then you can just balance it out with some bluffs like 99 with 9 of spades.
River
I think, you need to bet for value now, and your target will be hands like AQ, AJ, KQs, KJs, so something like half pot seems fine. As played he is clearly representing a boat, but even so I think, you need to make the call here. First off breaking down his range, I dont think, he has 44 or 66, because those hands would have been taken for a setmine preflop at least 90% of the time. I also dont think, he has K6 or K4, because those hands would have been folded at least 90% of the time. Finally I dont think, KK check back the turn and then overbet jam the river, and its only one combo anyway.
Which leaves us with AA and AK, and those hands make complete sense for him to have and play like this. But you block both those hands, so he can only have 4 combos of AK and 1 combo of AA for a total of 5 realistic nut combos, that he might play like this. Which mean that if you can find just 3-4 combos of something else, he is overplaying or turning into a
bluff, then calling is profitable.
And because this is a 33$ MTT, I really dont think, we can assume, an unknown opponent (at least unknown to me since you gave no info) never bluff in a situation like this. By checking to him again on the river, you have massively underrepped your hand, and he should also understand, that the A on the river is a much better card for his range, and that he can represent AA and AK by overbetting.
So I think, you need to assume, that he can be turning something into a bluff, or that he might be going for max value with trips or a worse flush thinking, that your range is capped. And for that reason you need to have hands, that check-call the river, and there is no better candidate for that than the nut flush. Maybe you could also have 44 or 66, which are nominally better hands, but since he either have AA, AK or a bluff/overplay, its better to call with AX of spades rather than 44 or 66.
If you dont call with the nut flush, then you never call at all, and this is highly problematic, if the opponent is capable of
bluffing. You are setting yourself up to be massively exploited, and this is not something, you want to be doing in mid and high stakes games. Maybe you can fold here in a 2,2$ MTT against a known nit, but in this spot you have to make the call and then just chuck it up to a cooler, if he happen to have it this time.