I have shot RH flinters as a LHer. However, the problem I had with the flash was due to the reaction of my Right EYE to the flash, and not my Left Eye looking down the barrel. I learned to close my right eye when shooting the RH lock( Some people can't do that), and that stopped the sometime flinching I experienced.
The Benefit of shooting a LH action as a LHer is having that stock block the view of your Right eye of the flash.( It works the same for RHers shooting a RH lock.) For some reason, the unconscious part of the brain( autonomous system) seems more comfortable shooting that way. If you learn to shoot with the locks on both sides of the stock, then shooting a DB flintlock poses no real problems, either. Not too many people have had the opportunity to shoot a DB flinter, however, me included.
There are two manifestations arising out of shooting a RH lock LHed: a. A serious Flinch; and b. Cross-eying, where at the last second, the shooter closes his aiming eye, and now focuses on the front sight with his other eye. As a shooting coach, you can stand behind the shooter, and you will see both the flinch, and the jerking of the barrel towards the other eye at the last second, which leads to a miss on the target.
Having the shooter close that other eye( the Right Eye in the case of a LHed shooter shooting a RH lock)usually helps both problem. It stops the second one.
Dry firing, and then firing only priming charge until the shooter ignores the flash with his aiming eye is the way to stop the flinch. Using a well-tuned lock that is fast also helps to get rid of the flint.
Practicing with light loads is the way to keep the flinch from coming back. You need to shoot at least 500 rds without flinching before the brain forgets about flinching. That seems like a lot of shooting, but you are trying to train " Muscle memory", in this case, mostly the muscles in your eyes. Dry firing can be part of this correct practice, so you don't go broke buying powder, flints and lead.
I hope that helps.
Paul