Generally speaking, if the stainless is not magnetic it is an austonitic stainless and can be soldered.
If it is magnetic it is a martinsitic stainless and soldering can be difficult.
You should use a flux which contains Zinc Chloride and Hydrochloric Acid. Fluxes with just Zinc Chloride are not enough to clean the surface to obtain the bond.
One of the silver bearing solders should work.
Although these contain silver, their melting point is way less than pure silver.
"Tin" the stainless first by applying a very thin coating of solder. It this won't accept the thin tinning layer, consider using an adhesive like Epoxy.
If the stainless will tin, then tin the silver part surface, assemble, clamp and sweat the two parts together.