I assume that the involving players are the hero, the BB and the initial BTN raiser.
Regarding the BB: He cold-called the preflop 3bet, then check-called flop and donk betted on the the turn. Looks quite fishy, yet his betting against 2 players looks strong, unless he is super-aggressive. His range should usually include a couple of strong hands (2pairs,straights,sets) together with strong combos (flush+pair, flush+gutshot,top_pair+gutshot, etc.).
Regarding the BTN: After raising preflop he is rather passive in a draw-heavy board. Some (small) percent of the time could be hiding a monster like pocket-tens,but most of the times he is folding to further aggression, if he is a solid player.
Your strategy: Assuming you play deep (~200BBs=400$), you have a very well covered flush draw and nut-straight-draw, which in case you hit, you can go for a very big bet in the river (you need to also evaluate the implied odds, not only the direct pot-odds). Also, you have the position on the OP, so in case he was betting with a medium-strength hand like T9o and a scary hard hits on the river, you could easily bluff him off, using a decent bet. Bearing in mind all these factors I would at least call (most of the times) and in some cases (depending on the OP) I would even raise (for the same reasons).