Well, not really... .999 silver is already refined. You will not get it any cleaner with Borax. In fact no chemical or heat treatment will make it purer. That can only be done electrolytically.
Bench scraps and filings should be fluxed with Soda Ash. If there is iron dust you couldn't get out, add a pinch of Salt Peter (Sodium Nitrate) to the flux. However, you should have first gone over the lot with a strong magnet to remove all the ferrous stuff.
I was a manufacturing jeweler and a precious metals refiner. But when I started out, one of my first experiments was with a steam casting (lost wax) setup I got at a gem and mineral show. That is an ideal setup for trials 'cause it's cheap. Used an electric "fifth burner" hot plate from a discount store as the burnout heat source, a flower pot for the oven, and a hand held MAPP gas torch to melt. Try that. I'm sure some hobby shop should have them.
BTW: the reason Sterling was invented was because pure silver is too soft. I would say practice with cheap old sterling, don't waste the fine silver. When the time comes to sell, Fine silver can be sold almost at spot price. Sterling always has a considerable discount.
