the furniture, however, has seen alot of love and is in great shape.
In that case, what is the need to apply any
additional finish to the wood? Sounds like you lucked out on the quality of treatment yr stock received over the years.
Now, as to using the linseed oil, I can tell you it works great on bare walnut--I refinished my first stock with it (100 yrs ago--well, OK, 40 yrs) and applied several coats, lovingly steel-wooling between coats. Rubbed the last coat with a rag. Stock still looks good.
And as you stated, linseed is good for refinishing over linseed.
Were I you, before messing up the stock of a nice rifle (if you just MUST put on more finish) I'd get hold of a junk stock with similar treatment, and try refinishing that. I might sand the stock first, then apply linseed, and rub it in THOROUGHLY, then let it dry for, say, several days--since yr stock already has lots of some kind of oil in the pores.
But my prediction is that the linseed will work just fine in combination with whatever organic oil was used on the stock previous. I also predict that you will need a LOT of rubbing on the stock to get the oil to penetrate. Warming the stock gently might be helpful too.
However, if the stock is really "in great shape," the question remains: Why add anything at all to the finish? Were the rifle mine, I'd leave it in the general shape in which the Russians released it. But that's me, and this is YOUR rifle. So, good luck in yr project.