I am on a slab and the my floor has a linoleum tile on it and I put a peel and stick tile floor on top of that. What is the best way to remove both old floors and what tools or chemicals will I need to make the job easier? I want to go down to the concrete to put in a new floor in. Will there be any concern for asbestos since the house was built in the late 80's?

No you should be safe from asbestos. You can break up the tile using a rubber mallet or a wooden mallet and a tool like a wood chisel with a wide blade a tool commonly used also to strip off wallpaper. After you get a few pieces of the bottom layer off you can push the edge of the tool underneath the pieces and strip off bigger blocks at a time.

Linoleum and peel and press won't warrant a hammer to break up, they won't shatter. . I think Wild may have misread your post a bit but the 4" scraper blade will work on the linoleum, the peel and press will pretty much pop off if you are under the linoleum. What kind of floor are you plannning to install, this demo may not be needed.

I was wondering that myself, why he wants to botter. Two layers of linoleum isn't all that thick. Maybe it has an embossed pattern he thinks will show through? I got a guide book printed in 1961 about installing these floors. It says when cold you can break it up with a hammer and chisel or warm the floor with an electric iron on a medium setting to soften the mastic holding it down. Also suggests a torch but I think the average person couldn't handle a torch indoors unless they are sweating pipes. And that book is from 1961 when they were still selling asbestos floor tiles as the latest and greatest. I'm thinking any floor that old that needs a torch probably would be asbestos and asbestos removal is not a do-it-yourself job.