With your Van floor covered with Kilmat it's not worth trying to glue anything to it.
Buy 5/8" 4x8 plywood, (I prefer the "Sanded one side) version. Put the worst side down and position so the butt joint is not down the middle of the Van where you'll be walking of crawling the length of the Van.
Ideally, in my opinion, I'd center the 4x8 sheet down the length of the Van and cut and fit pieces to fill in the spaces on either side going to the walls. (Or across the width with only one seam... either way...make a template). Once all the pieces are cut and fit, take them out, paint (seal) all the surface's, top, bottom and edges and reinstall when dry. You may choose to add adhesive to the edges of the smaller pieces to adhere to the larger sheets (don't paint those edges). If you have planned where cabinets, bed, etc are to be located the sheer weight of those items may keep some of those smaller pieces in place.
Add vinyl or whatever covering you want over the plywood. Glue it if you want. Or, my preference, just leave it painted and add a couple throw rugs that you can shake out as needed.
You may find that you need to screw a cabinet down because of where it's located. If so, Buy "L" brackets with a zink coating or stainless steel and use wood screws of the appropriate length to fasten to the plywood.
As mentioned, once you've added whatever you've chosen for wall covering like paneling, that should be installed to go over the 5/8" flooring you installed. Nothing is going to move on the floor and... If it's sealed, it won't warp.
just my 2¢