The best way to flatten sharpening stones is to lap them on plate glass that has had a bit of loose silicon carbide sprinkled on it.
Add a bit of oil or water (depending on stone type) to create a slurry.
This will quickly flatten water stones, Arkansas stones and even man-made stones (both aluminum oxide and silicon carbide). Ninety grit particles are about right for this process.
Plane bottoms have traditionally been lapped on soft cast-iron plates using a sequence of silicon carbide grits. A lapping plate should be softer than the item being lapped, so if you want to do a plane bottom, you can increase the effectiveness of plate glass by gluing a sheet of mylar film to it. The silicon carbide particles will bed in the mylar and abrade the plane bottom faster. Plain plate glass is fine for stone flattening, but the mylar helps appreciably when doing plane bottoms.