I was thinking give Umbreon a flame orb, and then bringing it in on something like scizor to cripple it completely, and then use heal bell. Would this work?
No, it wouldn't work because you are self-inflicting the burn status on yourself.
Synchronize passes on status problems to the opponent that caused the problem. Synchronize will not pass on the Sleep or Frozen status conditions, or if the status condition was obtained from items such as the Flame Orb.
Bulbapedia explains exactly. And it even uses Flame Orb as an example. It won't work
