Diamonds Are Forever?

I am about to start a thread that has never been done before. haha. I am just kidding. This is a similar thread to many of my others. I am looking for the optimal strategy. I will explain the sitation, what I did (and I think I am correct in doing so, but I want to hear the reasons against it), why I did it, and the outcome of the hand.
Middle stages of a live poker tournament. I played only strong hands or when in postion and managed to steadily increase from 10K to 30K. Blinds are currently 400/800 (15 min levels) and I have above average.
I am in the sb (30K) and action folds all the way to the button (15K) (button is a loose aggressive player as well as a calling station), who raises to 2400. I call with K10 diamonds and the bb (12K) (a very tight player but will play from his blind) calls as well. The flop comes:
398 diamond, diamond, and oh another diamond.
I check, and the bb leads 800 followed by a raise to 3K from the button. I decide to shove for my 30K. BB folds, and button calls saying "well I need to get lucky." Button shows AJ, A of diamonds and spoiler alert, he gets the Q of diamonds. A jack of diamonds was no where to be seen on the river.
Now, when I reflected on this hand, I said "well, I could have called the flop and then seen the diamond turn and maybe lost fewer chips. But then when I think about the outs he had and the amount of chips he put in on his draw to a diamond, I am satisfied with the way I played it. I need to fade a diamond (7 outs at most)
Should I look to get it in on the flop there since I am a huge favorite to win, (and get him to commit all his chips) or should I smooth call his raise and maybe be able to get away from the hand or save chips. However, I risk getting less chips in doing so. Should I see the turn and then push action, if a diamond were to not hit the turn.
Couldn't recover from that hand afterwards, and didn't make the money. Looking for your advice and as always thank you and see you around the tables!

You played it fine. I'm pretty much never going to be able to fold a K hi flush at this tourney stage with our chip stacks anyways.

Even if you slow play and the 4th diamond comes you have to put him on exactly the A of diamonds to find a fold. If you play it slow, He could just as easily have the Qd or Jd and so it's still REALLY hard to fold it.

You got it in good when you had a huge lead with some dead money in the pot, then he sucked out making a pretty bad call, actually he had almost decent odds to call...his reraise on the flop was stupid because it practically pot commits him. He should have flatted that 800 as he was being given a nice price to chase.

You played it well. But think about it from the villain's perspective. He played a decent hand in position. He's committed 40 something percent of his chips (15K - 2400-3000 = 9600 left). Villain can possibly win 20,600 (that's how much was in the pot and winnable by villain since you had him covered) by calling 9600. He calculates 9 outs (since he didn't know at the time of your shove you had 2 diamonds). He was getting ~2:1 on his call. The call wasn't great on his part but maybe he felt he was getting behind

in the distance playing K high flush will give u a profit, that's why it's good move

I would have done the same. Tournaments being what they are, you get in good when you have the chance.

If you could see the cards, you'd be happy to get your chips in on the flop. The exact sequence is less important than the fact you got them in good.