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.
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.
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.