For your primer coat, gesso works very well on soft plastics. It goes on gloopy, but shrinks to the details and is nicely flexible when dry. It gives a lovely texture to paint on too. It can leave air bubbles or bare shrinkage marks - just touch them up once the model is dry.
Do a couple of test models to get the consistency right, and it's definitely an overnight dry.
I've used Vallejo Surface Primer on soft/flexible figures too - it's quite thin, so you can get puddling. It also dries flexible and seems to hold the paint well, even though it's quite shiny.