Preflop, your raise was just fine. 8BB isn’t immense relative to the size of the stacks at this table, and that you got a call here from the big stack would be reasonable, since they can afford to throw away 800 chips on the off chance that you’re just trying to steal, although if they suspected that they should have raised you, especially with AA.
Their behavior is a little bit slippery. Limping AA is unconventional. Limp-raising would have made sense, maybe they only called here because your raise was so big. Maybe they did it to keep concealing their strength so you’d continue feeling comfortable betting. When you’re holding AA, you want your opponent to feel comfortable betting and loose as possible.
I don’t see the point of shoving the flop. The flop is terrible for you. It does nothing for you, and not that I’d have called with the cards that would have given me a straight here, but it’s possible your opponent could have one, though very unlikely.
It’s a safe enough flop that I think you should have lead with it, but why shove? The only call here is going to be a hand that beats you, and it really reads like a bluff. Which, granted, if your opponent is holding something weaker than you, QQ on down, maybe you want them thinking you’re bluffing so they’ll call. But it’s not really the best putting yourself at risk like that, with the turn and river to come, and your hand still unimproved from preflop.
You could have bet 2/3x - 1.5x pot and gotten the same effect, with less risk. If you get called, and of course here you would, you could still get away from the hand, slow down, or try barrelling a second time, re-evaluating your situation depending on what information the Turn card gives you. Another King? Hit that bet button. The card that landed? Well, I’d slow down and consider mucking the Kings.
Dumping KK (or AA for that matter) isn’t easy to do, but sometimes it does get beat. Either running into AA, or when your opponent hits 2-pair or better and your own hand doesn’t improve. When it happens, you need to be able to do it.