I wanted to do a coat closet in that other room and had wondered if there was a way to remove the tiles from that spot and reuse them in the bad spots. Don't know how I'd get them up without breaking them or how I'd stick them back down.
How many do you need to replace?
If they are the 9 x 9 vinyl/asbestos tiles (VAT), they are very brittle when they’re new, and they only get worse with age, so my advice is don’t even consider it.
However, if they are the 12 x 12 vinyl tiles, it’s like a lot of other plastic stuff, they have some flexibility, and if you warm them up, they can be even more flexible.
You never want to try to “pull” them up or “pry” them up. If you warm them up, and you pull or pry on them, you will just tear them apart. You probably have, or you can get, a 2 inch putty knife. With a belt sander, or a sanding disc on a drill, sharpen it like a razor. The concept is to slice them off the concrete, and warming them up makes them soft enough that they won’t break as you slice underneath them.
Use a torch to warm up the tiles. It will take a lot of patience because you actually want to warm up the bottom side, and the glue underneath them. So you have to warm them from the top very slowly. Obviously, you don’t want to burn them, but you want to get them hot just shy of burning. Then, use the putty/spackling knife to separate them from the floor. I am choosing my word carefully, “separate.” You don’t want to pry them up, and you don’t want a pull them up, you want to slice them off the floor. Don’t pull on them or fold them up at all, just let them ride up over your hand as you slice them loose, constantly heating them.
If you have an area like the closet, where you can pull them up, you probably have to sacrifice one to get to the edges of the others, but then this technique should work. You just have to be very patient, and go gently.
when you pull them up, they may be warped. If we’re only talking a few of them, I would prepare the places where they have to go down, put the adhesive down, and as you pull one up, install it in the new spot. If you have some kind of a roller, use that to press them down flat while they are still warm.
One last thought, if there’s a chip, or if there’s a little crooked edge, even a crack, You (and everybody else) is never going to look at it as closely as you are right now as you’re doing it. A little nick here or there is not the end of the world.
Hope it helps!