More importantly, you should have raised for more preflop. And you should bet the full pot on the Flop.

KK is nice, but vs 5 other players you're not favored. Make them pay to chase.

By the river, in your line, may as well put the money in. Its too big of a pot.

I also don't like the Turn bet, but I don't like checking either. OOP with an overpair is hard. You have to wonder which of the four is sandbagging or drawing or just calling with any random pair, lol