I dont really like chk call chk call as he never bets twice for value with worse hands. So he needs some bluffs, the only hands I can think that he might be bluffing with is a either 789* flopped straight, it's a great spot to turn 47** into a bluff cos he is completely under it vs ur range in fact this hand is the btm of your range now realisitiically so he makes mad equity by taking the pot at non showdown with 47. He would defo bet 789* once you;'ve chked but these are the only two hands imo
How often I expect him to bluff? In this instance I would say quite rarely purely because he doesn't really have enough legitimate bluffing hands and with no info on how he'd play 47/789* on the flop we cant even give the "air" side of his range any real weight, given that he RARELY bluffs with a flush.
I honestly think the best vacuum play here would be to chk/fold, but in terms for your range overall I'd be bet folding or bet calling depending on your analysis of his bluff frequency in this spot. As long as you are c/r 66 OTF then your range should protect you from getting bluffed too often imo if your villain is smart enough to realize that your legit bet/get in range OTT is pretty thin and is capable of turning most hands (even flushes) into bluffs OTT THEN id be merrily bet/calling because his legit stack off range OTT should be very thin also.
But I really cant see much merit to chk/call chk/call given that he is going to be playing kinda perfectly against us with that line, as in he will chk back flushes most of the time and Vbet boats all the time. If we're chking the flop I'm chk/folding the turn and betting the river for value if he chks back.
The bolded part seems to me to be quite a large underestimation of the combinations of hands he can bluff with that open the button in a heads up game and cbet and call a checkraise on this board. The justification for bluffing with 47 (which is a good and valid one) basically dissproves what you are saying. In other words, there are a load more combinations in villains range with LESS showdown value (think of things like overpairs+oesd, 24xx combos, 36xx with a draw, low flushes that might bet bet if he thinks you're capped <though people dont do that really) so if the bluff is good with 47 then the bluff is definitely good with those hands. In conclusion, he is probably bluffing more than you think. It's also not impossible for him to be vbetting a smaller flush that he's checking back the river with. Seems like a c/c then, the river is a tough spot but that doesn't mean you played your hand badly.