Before you use anything find out whether its acid or a strong alkali. Many wheel cleaners will strip the plating off callipers and fasteners and over time make the wheels paint work quite dull.
For me the best is clean them then add a coat of something specifically made for wheels, clean them every week with car shampoo and don't allow them to get into a state.
I don't know about Flash but most household cleaners are loaded with salt to act as a water softener.
Update, I have found that one ingredient in Flash is Bleach. Sorry but not on my car.
I wouldn't put anything on my pride and joy unless I either knew it was for cars and I had a good idea what's in it.
A work colleague used to put Fairy Liquid in his washer bottle, after a few years of this he had dull lighter streaks in the paint on his body work.