If you play a suited connector, maybe 5d6d, and you flop a flush, great(!), but how should you play it afterwards? Should you play it reasonably slowly in order to try and get as much value, or should you try and force a fold after the turn in case another diamond comes on the river and gives them a higher flush? Several times I've had a smaller suited connector hit a flush on the flop and then the turn or river has helped villain complete their higher flush (Qd, Kd, and so on).

You can safely assume that if an opponent also hits a flush then you are a loser. But, how likely will that be? With your 65dd holding and the monotone flop, there are 13-5 = 8 flush cards left out of the 45-card deck and 37 non-flush cards. Assume your one opponent holds one higher diamond. The chance another diamond hits is

Pr(diamond on turn or river) = 8/45 + 37/45*8/44 = 33%.

So, assuming you don’t lose to a full house of better, your winning chance is about 67%. Equilab has 68% for villain holding AdKs. With two opponents it reduces some. I used Equilab for the following example:

Hero 65dd. Villain 1 AdKs. Villain 2 Top 25%. Flop K 8 2ddd

Hero’s showdown equity was 66%, so he is definitely ahead but it’s not a monster hand. (I thought it would be a bigger reduction.)

With bets in pot size units and your eq > 50%, you can show that the minimum bet to have villain mistakenly call is as follows:

Bet > (1- eq) / (2eq- 1)

which, for eq = 66%, is a bet of about 1.06 x Pot. This give hero EV = Pot so villain is indifferent to calling or folding, a GTO-like characteristic.

Whether that minimum bet is superior to a smaller bet or to a slow play will depend on such exploitation factors as opponent characterization, stack sizes, position, tournament standing, etc.