re: Poker & jacks done by kings
"There are only three ways to play Jacks, and they're all wrong." -- Unknown
Seriously though, it's not at all uncommon for AA/KK to flat a raise especially if they're sure to take the flop HU. The only overcard KK is concerned about is an ace, and even that doesn't mean you have one. There's only a small range of Ax hands that people are 3betting with, and the only one he's behind often won't 3bet here for fear of chasing him out of the pot. Also, being a tourney rather than a cash game, a lot of players prefer to NOT get all-in with KK until they've seen what looks like a safe flop. Not saying it's necessarily a good strategy, but it's not uncommon. Some people even advocate folding AA pre in tourneys facing a spot like this (which I think is silly, but that's another discussion we've had a few times around here).
I don't think you played it too badly, but personally I will seldom put my deep stack or tourney life on the line with JJ facing strong opposition. Without knowing any stats on the villain, given his pre-flop raise and call of your 3bet, followed by this shove, he's telling you he's got strength. His shove here smells a lot like set or 2p, or at least the overpair it turned out to be. JJ may be an overpair on this flop, but it's still a vulnerable one. I think I'd find this fold pretty easy in this case, but that's just me. Cash game is likely to be a totally different story, though.