Roger Needham sells cut stones from Arkansas, still, and has a booth set up just inside the main gate at Friendship for years now. These are NOT carborundum or other synthetic stones. I have natural, cut Arkansas stones, at least one carborundum stone, and some Diamond "stones" I bought to test from Harbor Freight.
Roger told me that the quarry where the Black Arkansas stone- among the finest grain size-- has played out, and you now can usually only find similar grained stones in Green and Brown colors- NOT Black. The newer colors can be just as fine a grain as the older Black Stones, but you want to know your dealer, and do your own testing before buying.
As for finding flat stones in the wild- no, you don't find them often. But, stones are flattened by rubbing two stone surfaces against each other, with a bit of water to help move grit off to the sides, until the two stones flatten each other's high spots. Sandstones vary in grit size depending on what geological formation you mine. The same can be said for other rocks, including some shales.
How do you think those Granite grave stones get those highly polished surfaces on them? [ Mechanical grinders polish the surfaces using finer and finer grit stones, and water soluable oil to flush the waist grit off the stone. Pumice, in different grit sizes, and even rottenstone, as well as synthetic polishing media are now used to do the final polishing with powered buffing wheels to get that mirror finish.]