Paint for flexable/soft plastics?

Definitely prime.  Acrylics won't adhere well to that plastic on their own.  I'd use a lacquer-based primer, myself, for the best adhesion of the primer to the figure.  Acrylics or enamels should adhere well enough to the primed surface.

As to sealing, I would seal as well, though if you have a finished subject that has some areas that would be matte-like cloth, for example-and others that would be glossy-like glass or polished metal-it may make sealing a little more complicated, than just hitting the whole model with DullCote or with a gloss varnish.  I don't have any tip to offer there.

Also, someone mentioned Createx brand paints.  I've never used them, but I'm looking at their website now.  I agree with that other post, you should take a look, read the product descriptions, and see if any of their products might work for you.

https://createxcolors.com/

Would it be possible to substitute real cloth for the plastic cloth.   There's bound to be some old pieces laying arond that you don't need for anything else.  After you have it in the shape and size you need, you can stiffen it up with diluted white glue.  Paper towels acan sometimes be used if you happen to have a good supply stashed away.  You could also just attack the material or paper over the plastic cloth if it doesn't look to thick.

I have a model of Yoda that will make me face a similar situation in the future.

Although I've not tried this spray on flexi plastics etc I'd suggest the Krylon brand Fusion All in One spray.