Practice first.
The relatively low thermal conductivity of stainless steel is both a help and a hindrance if you are used to working with steel or copper. If you can target your heating closely the silver solder is much less likely to run all over the place. But conversely, when using targeted heating it's quite easy to leave potions of the joint a touch under-heated leaving weak spots or un-joined section.
If you do get it all well hot remember I takes a fair while to cool down naturally. Quenching to help is not a good idea.
Stainless discolours when seriously heated, motorcycle exhaust pipes are notorious for developing a yellow tint in use. Depending on grade and various specification details it can be quite difficult to get back to the standard shiny silver appearance if that is needed.
Like brass paint adhesion can be an issue. Decent key and appropriate primer needed.
As ever do things the right way with the right products and you will be fine. Its when folk assume that stainless is just perma-shine steel that troubles start. Up to a point you can. Its knowing where the point is and when to be specific that gets most of us into trouble.
Clive
(Who did it a bit wrong and had to scramble hard to get back.)