Thanks for the replies, all. I understand why I should have got it all in on the flop and indeed, this is backed up by analysis of previous hands I've played with KK and AA. In one previous instance, villain was able to make his flush on the river card because I let it get that far. A leak that definitely needs plugging.

In this hand, it turns out villain was holding pocket threes. I'm not sure whether he would have folded if I'd have gone all-in on the flop (given my lack of reads), but I see why it would have been a much better decision. I called his turn shove and lost the majority of my stack. Irritating at the time, but it serves me right and I'll definitely be learning from this.