Interesting spot because we are 250x effective. Having bet you have a very easy stack off in my opinion. Absolute worst case scenario against set + flush draw you should still have like 30-35% and you could easily be favoured against a draw or flipping against dry two pair or two pair + gutty.

As for whether you should c-bet the flop or not, I think checking and betting are both viable. There is an absolute cap on how low your equity can be, which means that your median equity is going to be pretty decent. I do think you have the potential to get it in good as well, if villain has some sort of mediocre combo draw he is probably not going to fold it.

plolearnerguy pretty much nailed it :)

Preflop i think this is kinda loose 3betting UTG+MP with such bad aces.

Postflop: Lets have a look at our range here

Slowplaying the best of our hands makes sense to me here. Hands like AdKQTd and AdKKTd or AdKQQd.

Then we have hands we are willing to stack off.
Hands like NFD +Pair+gutshot, or top set , or top two with OE.

Then we have medium strength hands that can take advantage from an equity shift to the turn i.e. AKQ type of hands.

And lastly we have hands in our Bet-folding range. Are we happy having a bet folding range here and if so is this particular hand falling into it?

Were we 100bb deep vs a single opponent i ld be happy having a polarised range betting half pot with mainly my whole range. Vs 2 opponents i feel obliged to completely remove the bet-folding portion of my range on the flop.

Being 250bb deep makes me want to modify my range further.
I dont particularly like GII on the flop here vs 2 opponents.
The problem with this particular holding is that i cant see myself folding if i get raised even if both players GII as we ld be folding too much equity. Most of the time one of our opponents would be holding a combo draw and the other would have 2p or a set. If UTG is the one with the set then we ld be playing for a 300bb side pot with only around 30% equity which basically means we would be close to a neutral EV decision point.
So i would rather check back the flop with this particular holding.
The problem with checking back is that on the really bad turns like K,Q,J,T without a diamond we have to fold to a jam but overall i think this approach is a higher EV line.