Rabbit skin glue with vinyl

​​Thanks for your patience, Hector – I’m asking a synthetic polymer expert your question and will get back to you.  Koo

Well, I asked the technicians at Golden Artists Colors, who specialize in acrylics – but, sorry to say, they don’t know about vinyl and rabbit skin glue.  I don’t know who can answer your specific question.  
It’s important to keep in mind that the inflexibility of traditional gesso is not primarily due to the binder; it’s due to traditional gesso’s high solid content (high PVC).  Animal glues are not entirely inflexible.  Rather it’s the chalk/gypsum particles that are entirely rigid.  Adding a bit of vinyl doesn’t change the fact that true gesso has a lot of solid particles; so, even if a bit of flexibility is added, true gesso remains fundamentally inflexible and should still be applied to a rigid support.  This is demonstrated by the several commercially produced, extra absorbent (i.e. high solid content) gessoes (Natural Pigment’s Tempera Ground, ArtBoards Gesso, Golden Artists Colors Absorbent Gesso)​: they have entirely synthetic polymer-based, flexible binders yet these gessoes are still prone to cracking if applied to flexible supports, especially when applied in multiple layers.
My understanding is that genuine rabbit skin glue is a bit more flexible than other animal glues – so it’s an option (albeit probably minor) when looking to increase flexibility in an animal glue ground.  Many glues sold as rabbit skin glue are actually pig and cow-based, so you have to research to find a true rabbit-based glue.  Buy from a reputable company who fully discloses and is honest about their ingredients.  
I’ve also read that adding a bit of glycerin (up to 5% by weight is the recommendation I find on line) to animal glue increases its flexibility.  Neither animal glues nor glycerin go through a process of polymerization; both remain indefinitely water-absorbent, and absorbency in a ground is a desirable characteristic for water-based mediums (not so much for oils).  The fact that synthetic polymers (such as vinyl) cure and become insoluble/water-resistant is a drawback in a ground designed for water-based paints.  I’ve experienced this myself in the high-solids, synthetic polymer-based commerical grounds listed above; even with their very high PVC, egg tempera paint wants to lift and misbehave a bit more on top of them because the binder turns into water-repellent plastic, so to speak (versus water-loving animal glue).  This is especially true for water-intensive methods.  However for oil paints it’s good to cut back a bit on the absorbency of traditional gesso.  Hence, how much it matters that vinyl decreases absorbency depends on one’s medium and working method.
Finally, neither animal glues nor glycerin “cure”, so in this regard they are more compatible than a synthetic polymer, which cures.  An important question is: does vinyl mixed into animal glue affect vinyl’s capacity to properly cure?  I suspect not, but I don’t know…  And I don’t actually have experience adding glycerin to gesso, my thoughts on it are speculative. 
In short, I can’t offer a definitive answer to your question, just some thoughts to ponder.
Koo