The hand history poster won't accept my hand so posting the old fashioned way.

Hero (BTN): 100 BB
SB: 99 BB (VPIP: 25.45, PFR: 12.73, 3Bet Preflop: 4.55, Hands: 55)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has Kd Jd
fold, fold, fold, Hero raises to 2.31 BB, SB calls 1.81 BB, fold

All standard here.

Flop : (5.62 BB, 2 players) 3d 5d Ks
SB bets 5.34 BB, Hero calls 5.34 BB

We flop huge and get donked into. I doubt we can ever fold our hand here so the only question that remains is 'Call or raise?'.
If we give villain all sets and all 8 remaining AXdd we have 44.56% equity. We have 29.70% equity vs sets and 57.56% against all AXdd hands.
Flatting allows us to see a turn card in position and we have showdown value. There's also not a lot worse that will call when we raise so we get rid of all his bluffs and are left with flushdraws and sets, maybe AA played weird. The bluffs he does have have little to no equity against our holdings.
A raise also changes a hand with decent showdown equity into somewhat of a bluff that never works. Because of his donking we'll also be able to make the size larger if we want to.

To me a call here seems better than raising but maybe someone has another idea here?

Turn : (16.3 BB, 2 players) 9s
SB bets 15.49 BB, Hero calls 15.49 BB

Turn changes nothing. If he had 99 or K9 somehow he has me beat now but still not folding. Don't think the turn is a spot we need to look at.

River : (47.28 BB, 2 players) 6c
SB bets 33.69 BB, Hero calls 33.69 BB

River is then another spot where our hand now is a bluffcatcher. It's unlikely villain does this with worse for value.
If we look at it from not being exploited we need to defend 1-A or 58.39% of our range. So we need to bluffcatch a lot here but our range is also very tight here.
We have all AXdd (without the K) and that's 9 combo's. We have some QXdd and JXdd as well. If we fold all of those we very likely need to call with every single pair we get to the river with?