After a few frustrating attempts of people activating Electric Terrain first turn, I can conclude Flame Orb does not work under Misty Terrain.
Calyrex is holding Flame Orb in this replay
Source
However, Terrains obviously don't work on not grounded Pokemon, so if you give a Flame Orb to a Flying Type or a Pokemon with Levitate, it will still get burned even in Misty Terrain.