Winching a car on a flat bed won't hurt a thing. Really, the only way to damage a car on a flat bed is if the tie down chains / straps are too tight. They will usually attach to the axles, control arms or use a strap unit over the top of the tire. You can express your concern about damage but don't tell the driver how to tow the vehicle. A reputable company will have qualified drivers.
If it is a local tow say around 5 miles and under 35 mph the tranny won't be damaged. I have personally towed thousands of vehicles on the drive wheels without damage. Remember back when these cars were new there was no such thing as a roll back/flat bed.