In my basement room, I have a painted concrete floor. That would be similar to your vinyl one.
I use a "portable" sewing table, which I found moved some when I speed sew. So I put a small rug under the legs/wheels to stop that.
Yes, my chair has wheels and it does move some so I am thinking about putting a small rug or carpet remnant under that to keep me from rolling backwards as I quilt!
Oh for heaven's sake, don't put a big rug down! I use minky quite a bit and that stuff gets all over the place, not to mention threads! Just leave the vinyl; it will help in keeping the floor clean or fabric dander.