Pre-flop: So, UTG limps, we have no reads on him. A standard range of small pairs, suited connectors, small suited aces and weaker suited broadway cards is standard here. 22-77, 54s+, JTs, QJs, QTs, A2s-A5s.
CO raises, it looks like he's trying to isolate the limper, so potentially his range could be slightly wider than usual. He's pretty passive though, so I doubt he's spazzing out with trash here. 44+, ATo+, A2s+, KTo+, K9s+, QJo, Q9s+, J9s+, T9o seems like a reasonable range for the CO.
The BTN calls, which probably means he has a hand that flops fairly well, and wants to see a multi-way pot IP. Could also have a strong, but not premium holding which he doesn't want to 3-bet against 2 players. Something like 88-JJ, AQo, AJs-AQs, KJs, QJs, 65s.
For us, in the SB with 3 other players in already, this is a clear flat. Seeing as a raise (unless it's abnormally large, but then we're risking too many chips on a bluff) isn't likely to push all three players out, we shouldn't do that.
The BB is going to flat with mainly with hands that play well multi-way, and quite wide because the price he's getting is good. 22-88, AQo, A4s-A5s, A8s-ATs, KQo, KTs, QTs, J9s-JTs, 54s-98s, 53s-86s. That seems like a reasonable sort of range to give him. He's getting good odds, but he's very tight so I don't think he's calling that wide.
Took a while, but those should be roughly what we can expect the ranges of all our opponents to look like here.
Flop: Now, the CO bets super-small when action is checked to him. From the stats we have, and the fact he's short stacked, he looks like a fairly weak-passive fish, who plays pretty fit/fold. From this, his weak bet is either a weak draw or a marginal made hand. We should flat here, because we want more players to stay in the pot, because if we make our flush we'll have better implied odds. We're also being given amazing odds to draw to our flush, so no need to semi-bluff here.
Turn: So, we go 4-way to the turn, and make our flush. We pretty much have the nuts, any hand that turned a boat would surely have raised the flop. Against so many players, trapping is rarely optimal. If we stick a decent sized bet out there, the chances that one of the players will have something he can call with are significantly higher than in a HU pot. I'm betting between 15-17BB. As it is, it checks round, and it's clear no one has much of anything unless they've been slow-playing. Ranges for all players are capped at a weak 9x who got scared of the flush draw coming in, but even that would have bet, I'd have thought (although the BB could have this because he's a nit).
River: Now you have to stick a bet out, and since you've disguised your hand, I'd make it a big one. The line you've taken could be a bluff, since no one has showed strength. I'd also stick out 18-20BB.
So, to answer your question again, betting the turn is better here, yes.