from The Century Dictionary.
- noun In glass-making, a stone or a slab of devitrified glass, fire-brick, etc., with smooth surface, on which the split cylinders of glass are heated in the flattening-furnace, and then spread out and made flat by the aid of the flattening-tool. Also called flatting-stone, flattening-plate, flatting-plate.
Sorry, no etymologies found.
First he warms it in the flue of his furnace and then, using his croppie or iron, he puts it on the flattening-stone; if you look carefully you will see that the top of this stone is covered with a large sheet of glass.
This done the flattening-stone was moved on wheels to a cooler part of the furnace and the sheet of glass upon it was transferred to a cooling-stone.