My experience with self stick vinyl tile -- I bought enough to cover 400 sq ft on concrete. I was hoping to just peel and stick, but after several tiles I realized these were in no way going to stay down on their own, they were not laying down all the way and I could pull them right back off easily. The floor was painted with flat latex, perhaps a primer would have been a bit better but even still I think the quality and amount of glue on the tile backing is what matters most here. Try one or two tiles first without applying extra glue, if its not really tight and flat on edges, the whole tile, and it peels right up with little effort, no good. What I did fixed the problem perfectly. Get some vinyl tile adhesive and get the proper trowel for applying vinyl tile adhesive. Important - Do Not substitute with something else here. The glue and trowel for vinyl tile are both designed to work for this application exactly. Ok so, a few things, the glue is VERY sticky, messy stuff, you will need some clean rags or paper towels work great and some mineral spirits or paint thinner, to clean hands and tools. A 4" putty knife to slap the glue down helps and your new trowel to spread glue evenly. Measure to the square foot and mark the areas one section at a time, spread glue in that marked area and let it set for several hours. It should change color and become very tacky, lay your tile down and it will grab snug and tight. Clean as you go, try not to get on your hands or tool handles. My new tiles look awesome, and are now glued down very tight and flat. Also, since you are using the extra adhesive anyway, assuming you are, you might want to consider non self stick tile if you can get a better tile or deal. It's not hard, just messy if you aren't careful, make sure you vent the room during install, scrape off any bumps, fill any holes and vacuum the floor first too. Good Luck.

Real good answer. Sheet vinyl or any other relatively thin and resilient flooring needs a smooth and flat substrate. If the existing tile job is flat with very little lippage, then preparing the surface to receive the new flooring would be easy and cost effective. As others have said, you must get a smooth and flat substrate or "slight variations in the surface will show through"...i.e. 'telegraph' to the surface of the vinyl.

You must have a smooth substrate for any resilient flooring material to look good for any length of time. You can smooth your floor with Ardex Feather Finish or an equivalent product, prime the surface with the primer recommended by the tile manufacturer and then install your new tile over that.

Unless you grind up the tiles and inhale them, there is little risk. It's "encapsulated (sealed in by the vinyl) Remove a few tiles and see how they were installed ... post pictures and we can figure out the best approach for getting rid of them.