CO = 61/26/13, BTN = 47/14/0

I thought of 3betting pre but flatting seemed fine too.  Is this a mandatory 3betting KK hand?

On flop, I decided to lead because it will keep CO honest and BTN probably won't go too crazy when I lead in a 3-way pot.  My hand is strong enough that I can x/c unless CO bets and BTN pots, but there's a lot of turn cards that can devalue my hands, so I'd rather start putting money in right now.

When BTN raises I'm kinda lost, I mean even vs {sets, 98 and JT98/QJT9} we have ~40% equity, but we probably aren't getting it in ahead at all.  That said, flatting doesn't seem like a good option because we will be forced to x/f on a lot of turns (sometimes incorrectly so).  But then again I don't really want to b/f this much of equity, which I think is a reason for x/c'ing on flop..?

Thoughts are appreciated!