How would I flatten a watercolour mounted on mat board?
So, first, I would probably take it to a professional restoration if there was no way I was willing to risk the painting. Likely to be expensive, though, but the safest approach.

If you want to try to flatten the support, you could try slowly wetting the back of matboard with sponged water, don't soak it, wet it, and then flatten under heavy pressure (carefully, you don't want to damage the painting) for a couple of days. This may bring the matboard back into shape, but it's a bit of a long shot really.

I have to be honest, though, if the work was one that I wanted to preserve, I'd be looking to a pro to do it.