Does BWC still stack?

[eisprinzessin]

First check out the descripition in Ulzuin’s chosen. It ONLY affects Stun Jacks, Grenado and Cannister bomb. And also need one point in each to activate.

You no longer need to activate all three skills, so that you can benefit of Ulzuin’s Chosen. Any one is fine, but of course it still applies only to these three skills.

The flat fire damage from BWC should work on each individual cast but the burn damage I doubt it stacks.

Correct, in order to stack the DoT and the debuffs (here: enemy OA, Armor and Resistances), they need to be applied from another source.

Buffs, Debuffs and Damage over Time
Damage over time (DoT) effects are different. Unlike debuff effects, DoTs stack from different sources and always do full damage. For example, if you apply Poison with your weapon, and then another Poison effect with a spell, both will deal full damage.

Grim Misadventure #54: Did You Know...

OA and DA reduction effects, such as Markovian’s Advantage, will refresh if the proc occurs before the debuff expires.

Grim Misadventure #70: Build 25 Preview

Two weapons [with the Plaguebearer’s affix] would be different sources, and those [Poison] Nova’s would stack. Same with the robe and affix.

If you activate the transmuter, your recharge time of 5 seconds matches with the duration of the debuffs.