Is it flat spots where the tires have rested on the "ground" or is it random flat spots?
I assume the vinyl tires are hollow?
They would need to be reinforced from the inside somehow to prevent them from getting flat spots again.
A car tire has a flat spot due to the weight of the car, the issue is the size of the flat area, since there is no air pressure in those vinyl tires the flat spot can't be adjusted that way either.
Has the softener in the vinyl tires affected the plastic of the rims in any way? Some vinyls turn styrene into soft goo ...
If it is a flat spot due to "ground" contact then maybe you could make a filler/support that fits between the rim and the inside of the tire. Something like the yellow part below.
The outer profile could be given a flat spot if you want the model to look more natural and not like a ballet dancer standing on her toe tips.
I suggest painting the areas where styrene touches vinyl with some enamel or laquer paint to prevent softener from the vinyl leaking into the styrene.
Make a few styrene discs and cut into segments.
/ Robin