Remove all grease. This can be by boiling with washing soda solution and then rubbing down with wire wool dipped in methylated spirit. making sure that you hands do not touch the work. These cold blue work best, despite their name "cold" if the workpiece is warm.
This can be by laying the barrel for an hour or so on a radiator or by pouring boiling water down the bore. Or by warming with a naked flame from a gas cooker ring or blowtorch. Even a blowtorch for creme brulee will work. To apply use long even strokes the full length of the workpiece. Allow adequate time to let the stuff work. Then rub off the "muck" with a grease free cottonwaste or rag or cotton wool and water. Then repeat the warming and atc. again.
Remember that hidden grease can ruin the "taking" of the chemical so your wire wool needs to be grease free, your cottonwaste or rag or cotton wool needs to be grease free and as you'll never get them grease free you need not to touch the work with your hands. For gun barrels the best way to handle is two tapered soft wood dowels tapped in one at muzzle, one at breech.m Use a craftknife to make the taper.
Be aware that acetone and/or carbon tetrachloride aren't nice to your skin. And acetone is a fire hazard. But, yes, when I did old school boiling and hot reblacking I did use acetone. You can buy it in two and a half litre glass bottles.