Usually flaking stocks are from the varnish that they put on at the factory drying out. I've done a fair share of wood working and usually it's just easier to redo the piece than fixing it up. Trying to clean up the flaking varnish usually leads to a blotchy look, and it will start flaking some where else soon. Unless someone else has found a way to repair it (which I would like to hear) i'd be easier to just redo the stock with Tru oil, tung oil, or some other finish.