Yup - its slate.

I love the flooring too and the best I've been able to match it is "Autumn Honed Slate". Honed slate means they gently buff down the top so there are not such distinct ridges in the slate surface, which to me, it looks like this slate pictured is honed. I have also seen a "Summer Buff" color which seems like a lighter slate like this variety shown and could be a close match too. It's so hard because there is such a variety amid boxes and samples so sometimes a picture of one - four tiles is hard to tell but I think in my mud/laundry I'm going with the Autumn. Good luck!

I love the Flooring!!

There is another Indian slate called Peacock that is in the same family at the Autumn.
If your using slate just make sure you check 5 to 10 boxes before you buy it to make sure 50% is not black. Make sure you purchase "Honed and Gauged. The gauging means that the tile is "almost" the same thickness . Clefting is natural on slate, the floor will cleft a bit even after it's been layed.
Maybe look at Quatz tile since it hasn't been quarried out like the slate has. It's very hard now to find deep rich colours in slate.
Beautiful floor if you can find it,

I think it's actually quartzite...Olympia stone in Desert sand