Shellac
Now my 2 cents. Actually free, personal opinion, and not really worth two cents.
I've refinished a few Fluesettes. I have found the unstained woods to be too light, and of course, by and large very plain in the field grades.
Also, if the stock is not reattached firmly, the 12's will break off the top of the stock at the top of the right shoulder. I must have a half dozen missing that chunk.
My advice would be to show your gunsmith a stock of a tone you like, and then have him match it.
Do not over finish (build too much film) with a Flues. They look stupid that way. They are not Citori's. Field grade Flues models have lots of open grain, and not much sheen. Thinly finished.
The Shellac can be toned as applied to take you to the color you wish. And shellac is soluble in denatured alcohol.
It's a personal preference of course, you may want a thick poly finish. But to me, as simple shotguns, the thin simple finish of the field grade Flues have a particular charm.