This isn’t technically an in-game bug, as the set appears fine in game, however if you equip the Fireplume Transmog Set, your character appears on the Armory and the Companion app in mostly underwear, with the only items visible being vanilla items, or Transmog appearances that are in the Armory database.
I attempted this on two of my characters to test the results.
To reproduce the problem, equip Fireplume Transmog and wait for the Armory to refresh character data.