How do you guys maximize a flopped flush?

I'm in BB with T[c] 8[c]. 3 limpers and the flop comes.

Q[c] 5[c] 3[c]. I lead 3/4 pot and get 1 LP caller who is fully stacked and avg. 28/8/2 ish type guy.

How do you play it the rest of the way when:

1) turn is 3[h] or
2) turn is a random brick like 8[h]?

Do not try this at home...

Stack sizes:
UTG: $461.00
CO: $447.10
Button: $745.70
Hero: $404.00
BB: $1.632.20

Pre-flop: (5 players) Hero is SB with
UTG folds, CO calls, Button calls, Hero calls, BB checks.

Flop: ($16, 4 players)
Hero checks, BB bets $22, CO calls, Button folds, Hero raises to $80, BB folds, CO calls.

Turn: ($198, 2 players)
Hero is all-in $320, CO calls.

River: ($838, 1 player + 1 all-in - Main pot: $838)


Results:
Final pot: $838
Hero shows 2H 7H
CO shows AC JD

A more serious answer is...lead all streets. Don't try to a check-raise as most villains will be cautious on a board like this unless they have a set or flush.

If the board pairs I would normally still value bet until I see aggression.

Keep betting 3/4.

Here's the problem. When I lead all streets and the board doesn't pair, they usually chicken out on me on the turn or river (even if I'm bettnig like 1/2 to 3/4 pot).

I'm considering just pushing any not paired turn. I think I'd get some sets/two pairs to call because they just couldn't believe I'd push with a flopped flush. The alternative is I win a tiny pot betting every street or lose a decent pot when the board pairs or another club hits. Hmm