Flush Draw Check, Bet, or Check/ Raise

I think a CR is a definite option here. If MP3 is a position aware player, his range of raising hands is much larger particularly after two limpers.

You have at least 9 outs to the nuts, and possible pair outs as well. The pot is large, and folding MP1 may allow you to take it down on the turn (in addition to buying outs to your 7) if MP3 peels and folds the turn UI. If not, you're putting in one big bet on the turn regardless due to your nut draw. If MP1 cold-calls with a weak K or other draw, you still retain a small equity edge in the 3-way pot.

The argument against the CR is that you may end up putting in three bets on the flop HU against the PFR.