The Exotic perk made me think of the jet pack wearing brother in Shield Brothers... Maybe from there? Also, the armor looks a bit like Cabal armor. The color is also similar to the mortar wearing brother.
Maybe you need to kill that brother last in that mission? Every time I've played it, he's killed first, as he's the one charging you. Maybe it has a similar mechanic to the Psion Flayer claims, as the drop is dependent on which boss is killed last.
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I got jade rabbit from mortar bro despite killing him first. The rest of the loot dropped from the other one on kill but I already had my exotic engram.