First of all there is a sub forum for hand analysis, so please post there next time. Anyways on to the hand:
Preflop
This is just an easy fold. Not going to go deeply into this, but until you get your freeflop ranges sorted and stop limping into pots from other seats than small blind, these mistakes are going to carry over to postflop and prevent you from seeing great results.
Flop
You got bailed out by flopping the nuts, which is obviously a great situation. Now its only a question of, how can you get your stack in the most profitable way, and there are two reasonable ways to do it. You can check with intentions to check-jam, if someone behind you takes the bait. The advantage of that play is, that it gives the players behind a chance to
bluff and the players in between a chance to call, if which case you "trapped" those chips in the pot. The disadvantage is, it might get checked through.
The less fancy and safer option is to do, what you did, which is to simply make a bet, when the action came to you. I do prefer a slighly smaller sizing though. When you bet full pot, you might scare away some
hands, that are drawing very thin, and that you want to get paid by. You still managed to get two callers though, which was a great result.
Turn
Not the best turn card, since it completed the flushdraw, but with less than a half pot sized bet left behind, I agree with your decision to get it in. Yes sometimes you will be drawing dead against a flush, but you are not going to check-fold, and I think, its more likely, that someone will call with worse than get it in themselfes. And for that reason I dont want the turn to get checked through, and now maybe god forbid yet another diamond rolls of on the river, and you end up losing to a hand like Q9 with the 9 of diamonds.
Results
The replayer dont show the results, which by the way I like, since it gives a more unbiased feedback. However you have kind of announced, that you lost the hand, so presumably someone either had a flush, or they rivered a better straight with AT. And whichever it was, this is just a cooler, or in the case of AT a bad beat.
Nearly all new poker players worry a lot about coolers and bad beat. And yes they suck, when they happen. But they are part of the game, we can not avoid them, and there is nothing to be learned from them. The things to be learned from this hand is, what happened,
before someone put a cooler or bad beat on you.
Preflop you should have folded, and on the flop I would like to see either a check-raise or a somewhat smaller bet. Some might say, that this dont matter, because you should not have been in the hand to begin with. But a similar situation could also occur, if you were in the blinds, and then you should be in the hand, and postflop would play out in a similar way. So there is still something to be learned from postflop, even if you should have folded preflop.