Flatting preflop is an alright play, but I as a default I think you are leaving money on the table with it.
Typically a SB vs MP vs BT squeezing range will be strong, most people don't bluff there too much (correctly so to an extent). With KK I think you should just try to stack his QQ/AK which he is going to have often instead of going for a slowplay which would be good against his 75s type of hands, which I doubt he has many of.
He does have a high 3bet over those 80 hands, so I can see where you are coming from. But I don't think that is strong enough of a read to change off of the default play of 4betting.
Flop is an easy call. Not easy in the sense of you are going to make a lot of money with it, but easy in the sense that it's clearly better than folding. If you just look at your equity on the flop it is going to be much higher than what you need to call, and I dont think future streets will be too much of a problem.
One argument which is very important is a consistency argument: By just calling preflop you are essentially saying "his 3bet range contains a lot of 86s K3s hands against which I want to slowplay". Now on this flop he will certainly cbet almost all 'air' hands. So KK is doing very well.
Another small argument is that I often see people check the flop with Ax hands that were bluffing preflop.. A3s and so on. You have probable done so yourself. So I think you are actually in much better shape on the flop than you think.
8♦ and fold 9 
9♦ for backdoor reasons.