I don't think you can blue a stainless barrel. I believe that the bluing or browning is a chemical reaction (an oxidation of sorts) between the bluing agent and the carbon steel. Stainless has a different chemical composition with more chromium and moly in it as well as other alloys which resist oxidation. There are some forms of stainless which will rust (400 series). But the stainless alloys used in barrels are fairly weather resistant and probably won't take a bluing.