Could a skid steer be used on this without damaging it? If so is there any rubber flooring that would hold up to a skid steer?

You could use a Skid Steer on our 1" Horse Stall Tiles. As long as the bucket was not used on the tiles, you could drive back and forth on these tiles with this machinery as much as you like. We do offer a wide range of hard plastic tiles too that would be good for driving over them with a Skid Steer Loader as well. You can find those products on our garage floor tiles page.