Soldering stainless steel is tricky, because the reason that stainless steel is "stainless" is a protective oxide layer.
Using flux designed for copper may not work well, or at all, becasue copper oxides are more easily removed.
While the joint needs to be "hot enough" to work, "too hot" is very possible and generally requires starting over from scratch, since it burns off the flux.
For soldering (on anything) to succeed, you need the joint to be mechanically clean (scrubbed, sanded, wirebrushed) to remove dirt and major corrosion. It needs to be chemically clean (removal of thin oxide layers with flux) and it needs to be at the right temperature (the metal of the joint should melt the solder, you should not be melting solder with your flame directly.)
At the correct temperature and with a properly clean joint, the solder should wick into the joint by capillary action. That will not happen at ANY temperature if the joint is not clean.
The above holds true both for "soft solders" (true solder, below 800F) and for "hard solder" (technically a brazing process) also known as "silver solder" - which was less confusing before there was low-temperature solder with silver in it, as lead-free solders became the norm. The fluxes and temperatures differ. The common lead free solder of the food industry was 95-5 tin-antimony before those other solders came along.
If not using stainless-steel-specific flux, you can sometimes succeed by wire-brushing with a liquid or paste flux on the joint, as the flux will prevent or reduce immediate attack by the oxygen in air after the bristles scrape it away, and then you can heat and solder immediately. Better success is had with stainless steel specific flux. Any flux residue should be removed by through cleaning afterwards (stainless is common in food-service equipment, so solders, fluxes and cleaning processes suitable for items in contact with food are plentiful in the marketplace.)
Alternatively, the item could be Tungsten Inert Gas welded, by a skilled operator (not a job you want to try for your first one - it's tricky welding thin stuff) - again, common in foodservice. Restoring the color and passivating (removing free iron, typically with citric acid) the surface in the "Heat Affected Zone" are normal post-welding processes.