I have a 12 year old Browning Citori XS Sporting that I've used for sporting clays quite a bit. It has some deep powder burns on the receiver....

What is the best product for getting rid of the staining?

Wade,

I'm no expert on the subject, but I would first saturate with a solvent, Hoppes,etc..., then use Flitz metal polish with a soft cotton rag. Flitz has been effective for me in removing the fouling on the cylinder face of my stainless revolver. Elbow grease and patience are required!

Try Ballistol.