Do I need to remove old stick & peel tile before laying new floor?

Have you already purchased it?

Be very careful with laminate in the kitchen, floors don't stay dry, water spills, drips when doing dishes, etc. can do harm to laminate as it sucks up the water and expands if it isn't caught quick enough or the seams not dried. You can probably put it over the peel and stick, but make sure the floor is very level.

Hello Mary! If the old tiles aren't sticking up anywhere, you only have that one layer of flooring, and you are installing a floating laminate floor you can install over the peel and stick tiles. You may have a height issue in doorways and trim because you are adding another layer of floor. You can take all your wall trim off and replace it after you have installed the laminate and you might have to make some cuts in the doorway trim to slide the laminate under that trim. Of course it is always better to remove the old flooring. You can heat up/soften up the tiles with a blow dryer and pry them up. I have used a heat gun set on low as well but you have to be more careful with that. It is amazing how stuck on peel and stick tiles can be! It can be quite a job to remove them especially if you have a large area.

Yes you can. You will need to use the manufacturers recommended underlayment. Personally I loathe laminate flooring. Joints can separate over time. Swells if it gets wet. Edges can easily chip. Just a few. I always recommend peel and stick vinyl planks for kitchens, baths, and basements. Waterproof and resilient. Looks like ceramic, porcelain and wood.

YOU CAN DO IT. Please post you project when you do it.

I would as a preventative as the glue can stop working with age. Go the extra step and make sure all your hard work inlaying the tile is not wasted.