Yo frank !!!!!!!!
Guru1911 here for you:
Excellent & unique bolt action rifle--forerunner of the rem model 7. Don't get rid of it---very handy when shooting from an elevated tree stand. Btw: Syn stocks do not exist for this rifle !!!!
Yes, the old finish is flaking & the old finish needs to be removed. For the present time, this will help to keep the flaking under control:
1. Gently rub stock with 4-0 steel wool until all the flakes are gone.
2. Get a small can of min-wax clear polyurethane finish. Wrap a cleaning patch or cotton material around the tip of 2 of your fingers & gently dip into the solution---just a few drops each time.
3. Beginning at the butt end of the stock, rub in a circular fashion until the patch is almost dry. Dip & repeat in another area until the stock is covered.
4. Hang on a nail in a warm area of your shop or in the house until the smell of the poly is gone. May take several days depending on the temp. You can speed the drying time by blowing hot air from a hairdryer on to the stock.
5. When completely dry, gently buff stock with a clean piece of steel wool. Then rub a coat of johnson's old fashioned paste floor wax on the stock. Let dry to a haze & buff off with a clean terry cloth towel.
There you go---40 years of practice in a few sentences. Thanks for allowing me the opportunity to help you with your situation.