I think your opponent played really well. As for bad beat or misplay? A little of column A, a little of column B. You were unlucky, but there's a small chance to get away from even KK here.
The flop 3 bet from you gave him the info that you had the type of hand you did. If he was on a bluff, it would be extremely rare for him to call your reraise. He'd just fold immediately as the message your reraise sends is "I'm never folding". The fact that he called meant he wanted to get it all in but didn't want to scare away hands like pocket 10s or AQ so he gave you time to get comfortable with your hand by letting a turn card come off.
You said your opponent was known for bluffing. Be VERY cautious when somebody known for bluffing just calls a reraise post flop on a dry board. It generally means they actually have something very strong and don't want to scare you away for once. As crazy as it sounds on the surface, if you think about it from their point of view, a bluffer will almost never flat call a 3 bet to bluff later and you should consider check-calling or check-folding, even with a hand like Kings. They're aware your 3 bet means you're never folding, and if they bet later anyway, they either don't know when to stop or are EXTREMELY strong.
If you've seen them demonstrate that they know when to fold in the past, then this is a painful check-fold spot after they flat your flop 3-bet on a dry board. Their range pre becomes very pair heavy when they're interested in a dry board this much, which makes their holdings very set heavy or even AA. I believe their 10s-KK range would worry about being outdrawn by your theoretical Ace highs and reraise, 4 betting you all in on the flop, which you could comfortably call.
It's a very rare spot to be in. I don't hate your line at all, betting out on the flop because the c bet is often interpreted as a bluff by aggressive bluffers anyway and they'd raise you the same way they would bet into you if you checked. I think your play was perfect, and you get max value from bluff raises by repping a missed A high continuation bet, it's just very hard to humble yourself to somebody with a loose image having a killer hand. But the action clearly dictated that when they were comfortable flatting two raises. People who bluff tend to think ahead and plan more often than average players. If they still have a plan for winning AFTER you 3 bet them on a dry flop that involves just calling, you're probably already drawing dead to a set of kings.
Their mindset would go something like this:
When you bet: Let me raise, I'd raise if I were bluffing so he might call hoping for an ace, or even reraise me.
When they raise, and you reraise: Wow, I hope he has a hand. He put in a lot of his stack. He might have AK and be angry though. I don't know if he'll call my all in with just AK. There's no obvious draw and I want more money. I'll just call and wait for him to attack my image, or I'll bet when an Ace comes out.
It's a VERY difficult thing to see in real time, and slightly counter-intuitive on the surface, but if an aggro bluffer isn't trying to put your overpair all in when you 3 bet a dry flop, you're probably losing. If they're 4 betting all in, it's an easy call. I hope my explanation wasn't too abstract.