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I was trying to figure out what he was holding. And you figure it out by his actions.

He cold called 3 bets pre-flop. On a .5/1 table that usually narrows the hands down to AA, KK, QQ, JJ, TT, AKs and KQs. Then he called me down to the river.

Based on my play he had to think I had an A, so if he couldn't beat an A why bet the river? The board paired the K and the flush draw got there so it is very possible he made his hand.

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This is all fine except that you're giving your opponent way too much credit.

Villain is already known to be an donkey because only donkeys call three cold on the flop. It follows from this that villain wasn't spending a lot of time deducing that you must have a made hand by the river. He was just thinking about whatever it is donkeys think about during the hand, which probably involves little cartoon figures dancing around in a thought bubble or something. On the river, you checked to him and he interrupted his donkey-dreams to think "I have an ace + there's an ace on board = bet." Or "maybe he'll fold if I bet my 66." And he ended up being right because you out-thought yourself.

Most villains aren't very good poker players. Villains who call three cold on the flop definitely aren't very good poker players. Inferrences that you draw on their behavior that are based on an assumption that your opponent plays like you do will very often be wrong, and they'll very often cost you money. In this case, I'd say there's about a 60% chance that you folded the best hand.