Does anyone know if tile can be put down over painted concrete flooring

It is not suggested that it be done, unless the paint is worn down. You must test the paint adhesion as once the thinset goes down it can cause the bond of the paint to fail. Thus the bond of the tile to the floor to fail as well.

You can simply put some water on the floor and let it rest there for a few hours. If the paint begins to bubble, then you have your answer. But any gloss must be removed prior for proper adhesion.

You can rent a machine that will remove the paint surface at the local rental center. It uses either stones or a cutting tool to scrape the floor down. Its a dusty job but will remove the paint quite quickly. You can always use a acid wash as well.

Don't install tile over painted cement.
Remove the paint by mechanical means.

Matt
tile contractor