Gorilla Glue products will not dissolve vinyl.  However, since vinyl is a petroleum based product, it will depend on how much petroleum the manufacturer used.  If they used a lot during manufacturing, our glues will not be able to get a secure or tight bond since the surface is too slick and oily.  If it is a lower amount, they will work great.   Therefore,  this specific type of application will be trail and error.   I would recommend scratching up both surfaces first since both surfaces are also non-porous and personally, I would try Gorilla Super Glue first since you do not have to clamp the surfaces together while the glue is curing.

I hope this information is helpful!