If you're not in a position to change the slate/tiles (which look to be in perfect condition!) you can certainly go with gray walls and white trim, but the gray will need to have brown or green hues to it. With the right gray, it will look sensational.

Here's some ideas from the gray family that would work with your slate/tile flooring.

Left: Benjamin Moore Edgecomb Gray
Right: Behr Dolphin Fin

Christi, on behalf of Thos. Baker

Also....Benjamin Moore Revere Pewter.

Christi, on behalf of Thos. Baker

I do not know for the gray color,because flour tiles, maybe some kind of brown, or olive ...