Scenario 1:
If we have e.g. T

9

and call preflop vs open raise OOP. flop comes e.g 2

5

K
and we cc flop and turn. On river if we hit flush, I am wondering if we need donk range.
When flush comes on river, the fact is that most of the draws from villian range did improve, meaning that on river when he bets he doesnt have so many bluffs to bet (unless he turns hands into bluff which is imo not optimal). Also if we check he will bet hands that he has value vs our range, so it will mostly be flushes and maybe 2 pair+. With Ts9s, we cant even value raise so we mostly cc and this way protect our check range. He would surely check back hands like pairs which is mayority of villian range.
So the main point why I would donk flushes (especially lower) is because we cant cr them, and because we dont expect villian to bluff frequently once we check. So if he doesnt have so many bluffs in range on river, then he really cant exploit our top pairs, 2nd pairs by betting, so imo we dont need to protect check range.
Off course big benefit of having donk range is that we can bluff some 2nd pairs with flush blocker, or bluff some busted OESD, which we would have to give up if we have only check range.
Scenario 2:
Another scenario would be when flush comes on turn. In that case, villian has many potential bluffs (any spade fd or even other bluffs since it is scare card), and thats why imo it makes sense to check mostly flushes. We can off course donk lower flushes to avoid seeing another spade and check back. So in this scenario I would mostly check flushes on turn and river.
For scenrio 1 and 2, the same applies when straight completes, especially 4 card straight or 4 card flushes.
Scenario 3:
We hold TJs and call preflop open raise OOP. Board is T

Q

2
We cc flop. Turn comes T
Now many villians will pot control top pairs either turn or river, so we will loose value by checking. Also many villians will not bluff often, because they pot control top pairs, so they cant value bet so many hands.
So again imo good spot to donk draws and Tx. If we have some weak kicker, off course we can use smaller bet sizes.