Preflop, i think it's fine to play a hand like this in strong position with strong high possibilities. (top 3 broadway, 2 fds, one nut)
Forget the A6 for low aspect of your hand, it sucks. This will so rarely factor into how you play the hand it's almost useless. You are playing this hand to hit a nice high flop such as wrap, nut flush draw, 2pair, trips, str8 etc.
Flop. I think this is a bad call. No 1 there's no doubt the flop has come badly for you. 2 low cards when you're looking for a high flop. Your only draws are backdoor ones. If he bet smallish, like in the region of a min bet, I might be inclined to take a card and try and hit a favourable turn card such as a HIGH club, or a T, Q or K. He doesn't, he bets pot. I would fold here.
Turn. Ok so you've hit a K on the turn. Are you good? To be honest you don't know. You're making a bit of a stab in the dark now by calling. Your call on the flop has left you in this predicament. This is player dependent but in most cases you will be behind here, possibly to a set or 2 pair. If your pair of kings are ahead you can still be in not great shape for example vs a low wrap and fd, pair and lnut low draw + fd etc.
Not to mention that he could just have the nut low + a pair or something and when he hits, he can pump his big 2 way hands on the river the same as just the nut low, so you'll effectively be calling off all your chips in the dark with possibly just top pair. I'd say this is usually a fold too if you find yourself in this position.
You do of course have a tiny draw to the nuts. You never know!
You had him on AA34. Here's your equity vs this hand calling a pot size bet on the turn.
As

0.175

Ah

0.825
River? Insta - call. You've come too far to be folding the nut trips now so call immediately and hope you're good!