Ok I misread what you were trying to use the AK of clubs to represent. I don't know why you did that instead of just a regular simulation but here you go:
ProPokerTools Hold'em Simulation
21,804,741 trials (Exhaustive)
board: K 7 6
8d 5d 27.09% (5,862,881 wins, 88,483 ties)
20% 24.87% (5,244,406 wins, 360,035 ties)
K9-KQ, AK, K7s, K6s, 76s, QQ-66, Ac*c, Kc*c, QcJc, QcTc, Qc9c, Qc8c, JcTc, Jc9c, Jc8c, Tc9c, Tc8c, 9c8c 48.04% (10,288,806 wins, 372,257 ties)
note that I used top 20% for the first bettor's range since he raised preflop and c-bet, it might be a bit more narrow than that, feel free to tinker with the sim.
So no matter how we arrived at the number, I'm fine with agreeing our equity is somewhere in the high 20%'s and its going to depend a bit on exactly what ranges we assign.
13:2 on the flop are our immediate pot odds, and we have 27%ish equity, those are the relevant numbers. You seem to be mis-understanding the way pot odds work. "Equity" is equity, its our % chance to win the hand accounting for all turn/river combinations against the ranges assigned. I think you are arguing that even though we are getting 13:2 to call now, if we miss on the turn we will have to call another bet (which we will again be getting proper pot odds to call). These add up to make the *effective odds* worse than they appear. This is also called 'reverse implied odds' - these things are straight out of Theory of Poker. What you are neglecting to think about is that part of our equity on the flop comes from the times we just go ahead and hit our hand right on the turn, and heck sometimes they are even drawing dead once we do, and bets are still going to go in. These are 'implied odds'. In some situations its easy to argue that RIO trump IO by a substantial margin, and in other situations its less clear. But even if there are more RIO than IO here it is far from enough to overcome the immediate price when we have 27%ish equity. If our equity were more like 18% it would matter.
You are doing a lot of your analysis incorrectly, and your appeal to authority to Mike Caro is meaningless to me. Either you are misunderstanding something he wrote, or he wrote something wrong. I don't need anyone to tell me that when you start by saying a flush draw will be out 40% of the times based on the hand distributions you assigned (a somewhat unnecessary exercise in the first place), and then you round that up to 2 out of 4 people will hold one (40% became 50% just like that!) and then use the 50% number in your subsequent equation, that you are estimating incorrectly and in your favor. If we accepted your initial combo counting (I already explained why its incorrect which you ignored in your subsequent replies), then the chance that someone holds a flush draw in clubs with 4 opponents would be exactly 40%, not 50%: 40% * 4 people / 4 suits = 40%.