Wow, that is a tricky question as most of the manufacturers don't really make a mat for vinyl flooring.
Do you have the hook in the front to keep it from sliding around? Many of the mats come with "nubs or spikes" on the backside of the mat and that usually adds to the sliding issue.
I have vinyl floors in my truck and I put in some Fanmats (Virgina Tech of course!) but they do slide around a little bit. I have heard of people adding that stuff you put in your kitchen shelves (thin rubber sheets?) under their mats, or gluing Velcro strips under the mat to keep them in place but easy to remove for cleaning. I even read about someone putting carpet underneath and then putting the rubber mats on top but there could be some thickness issues. Safety is the top concern as you don't want to have any interference with your pedals!
Let me look into this a bit more and I will get back to you.