Hi Welcome to the forum. I suspect you will be having more problems than just not flat.
The flattening process, not matter how it is achieved will almost certainly cause about a zillion micro-cracks, or worse, visible cracks in the hardened section. Either way chunks will almost certainly fall out after a little use.
I have visions of the flame hardening as a man with a gas torch and if so, the project was doomed before he lit the torch.
Two things I can suggest for the next ones.
1:
Maybe look at relief slots in the back side of the ring so that the heat treatment process will allow the metal to move a little and minimize any distortion and it can then go straight to the grinder.
2:
Control the heat treating process better with multiple heat sources and maybe even rotate the ring as it is heating and soaking.
I sicerely hope that someone can chime in and help you, but I suspect the fate of this project was foiled at the onset.
Sorry to be a doomer and gloomer.