Yes, I should have said that you may have a difficult time with hard solder rather than saying you may not be able to do it. It is do-able, especially on small rings. The metal absorbs the heat, so the larger the piece is the more heat is absorbed by the metal. This means there is less heat to melt your solder. As long as you keep your work small, you should be fine. I also use this torch for small work. It's surprising how much you can do with one. A simple plumbers' propane/mapp torch from the hardware store will do the trick if you find you need more heat.
On flux: A lot of people make their own flux. You can Googgle "Pripp's Flux" to find a recipe. I found it pretty easy to make. My-T-Flux, a commercial flux, is recommended for Argentium Sterling, but I don't know why or what's different about it. I'd be interested if anyone knows. Handy Flux, a paste, is also very popular for most work.