Tile will stick to most rigid level surfaces including painted wood provided the correct preparation work is done to ensure the adhesive or mortar will stick to the floor surface.
Adhesive tiles on painted floor.
Repair any gaps cracks or holes in the existing floor by cutting.
Unfortunately the tile cannot be adhered directly to the painted surface.
Resilient vinyl floor tiles that are installed with adhesives come in two types.
Once the concrete floor is paint free the tiling process is similar to most other floor tiling jobs.
All paint will need to be removed before you begin installing the tile.
But remember that any small bumps or cracks in the floor will show through the tiles.
Those that are glued down with a separate adhesive that is spread onto the floor with a notched trowel and those with pre applied adhesive covered with a backing that is peeled away to install the tile.
As long as the surface is smooth go ahead with the vinyl tiles.