The flakes coming off are iron oxide. The Japanese save the flakes, grind them into a fine powder, and use it to polish their blades.
The amout of carbon in blade steel is .60 to 1.00% so a 8oz. blade has about 2 grams of carbon. The drop in total carbon content is probably less than a point or two in a normally forged blade.
The carbon loss in forging is very minute and restricted to within a few ten thousandths of an inch of the surface. This area is exposed to the free oxygen in the atmosphere of the forge. Any carbon that combines in this zone becomes gaseous carbon mon/di-oxide. The thin carbon depleted layer is called the "skin", or de-carb. The rest of the carbon in the steel is still locked up in the matrix of the molecular structure.
Controlling the forge atmosphere is how to limit carbon loss to almost nothing. Balancing the gas/air mix to be slightly reducing or neutral is how that is done.