Many, many years ago, while working in Propulsion at Boeing, I was recruited for a job at a simulator manufacturer. At the time I was rather unhappy with Boeing so I took their factory visit (expense paid trips are seldom a bad thing
). The short story was they were primarily interested in my 'real world' propulsion experience, and figured they could teach me the simulator stuff in short order.
However their description of what I'd be doing left me cold - I don't know if they picked up on that, or it was just they weren't that in to me, but the offer I got was disappointing and I said no thanks...
Anyway, I don't know of anyone other than the simulator manufacturers that actually train for that. If you get meaningful real world experience in how aircraft work, they'll happily teach you the rest.