Scrapping and burnishing for sure. I don’t know about stain. Perhaps someone that has handled a lot of originals could answer this question.
Most definitely not linseed oil. This subject comes up fairly regularly on this site, so if you search a little bit, you will find many, many conversations.
Linseed oil, by itself, is not now, nor has it ever been a good gun finish. It is neither waterproof nor durable, and it takes forever to dry. I’ll give you the 10 cent tour.
First of all, linseed oil doesn’t dry in the sense that a water based or alcohol based solution dries. With water and alcohol, the solvent evaporates, leaving behind whatever was dissolved or suspended in it. Linseed oil doesn’t do that – it polymerizes. That means that the individual molecules that comprise the oil react with oxygen in the atmosphere and become linked to each other, or crosslinked as we say. When this process is complete, what you have is essentially a single giant molecule.
You can speed up the polymerization in several ways. You can heat the oil, which partially polymerizes it, you can add a chemical catalyst called a drier that speeds the polymerization, or both. Modern driers are typically cobalt and manganese, historically lead was used. Once you’ve heated the oil and added the catalyst, you now have what’s known as a drying oil, or “boiled” linseed oil. Boiled linseed oil polymerizes much faster than pure linseed oil, but it still isn’t a very good finish. For weather resistance you need to add a resin.
If you add a resin to a drying oil, you now have a varnish. The properties of varnish are highly dependent on the resins one chooses to use, but they can be very weather and damage resistant, and have properties that make them much better gun finishes that most of the modern finishes used today.
The gun builders in the late 1700’s had many types of resins and hence varnishes available, and I doubt that anyone knows exactly which varnish was used on any particular gun. However, if you search for brown varnish on this site, you will find recipes for making a period correct varnish that is either very similar to or identical to the finish that would have been used on the gun you are building.