I'm given to understand that a phosphoric acid flux is available for stainless steels, too. Phosphoric acid is not a strong acid, insomuch that it's pKa is low compared to other mineral acids. As a result, the degree of hydrogen liberation is lowered and the phosphate coating it provides ensures directly below it that the metal is atomically clean for wetting. It would be a better choice, but in the event you can't, it is a safer choice to make up a standardised 'killed spirits' flux for stainless steels that contains very much less strong acid.
A good recipe is : 32g zinc chloride, 5g ammonium chloride, 4-5ml of HCL (32-37%), topped up to 100ml with clean water.
The susceptibility of a given corrosion-resisting or corrosion-resistant (I try not to say 'stainless' with my professional hat on, because goshdarnit, even gold corrodes in the right medium) steel to deleterious effects from hydrogen gas is dependent upon its microstructure. As you've rightly addressed, AISI/SAE 3xx type 'stainless' steels are relatively soft, don't achieve very high strengths except via considerable amounts of cold work, and have good-to-excellent corrosion resistance - and they are essentially immune to hydrogen embrittlement.
The 3xx series are austenitic stainless steels, with a face-centred cubic atomic lattice with manifold low-energy slip systems available for deformation in a very close-packed lattice. As a result, diffusion of even a molecule as small as diatomic hydrogen is very slow, preventing buildup of substantial quantities of the gas at high-energy sites such as grain boundary triple points. Furthermore, as the activation energy for slip systems is low, any local microconcentration of stress, such as a hypothetical pocket of diffused gas would begin to lower as soon as generated, by the readily mobilised dislocation structure of the metal.
Most 3xx series steels are stable austenite, meaning they go through no microstructural transformations with temperature, and are therefore only strengthened by work hardening, which is removed by annealing effects such as exposure to welding and jointing heat. Their stable austenite is due to very heavy alloying concentrations of chromium and nickel. As an interesting side-note into the role of solute drag in transformation physicochemistry in steels, a total alloying concentration of chromium and nickel causes complete austenite in steels well below the requirement for nickel alone. Chromium destabilises austenite on its own. The atoms move in mysterious ways...
3xx series steels corrosion resistance is due to the presence of both chromium and nickel in high percentages and so the adsorbed spinel surface oxide is robust. Additions of molybdenum and nitrogen further enhance it and to much greater effect, as well as increase the strength of the alloy extremely markedly in the latter case. There are a range of very high strength austenitic steels with nitrogen contents as high as 0.5%.
Now, the 4xx series steels, both martensitic and ferritic, and the 6xx series steels, the preceipitation-harenable grades both martensitic and austenitic, are designed from a different angle. While 3xx series steels are expensive and intended to offer premium levels of corrosion resistance with good strength, martensitic steels and especially precipitation-hardening steels are intended to provide a degree of corrosion resistance commensurate with the cost of production, at a target level of strength. Usually as strength increases (due to carbon content) corrosion resistance falls, although that is not always the case.
As a result the corrosion resistance of a given high and ultra-high strength steel is a compromise. The more recent the development of the steel, oftentimes the greater its corrosion resistance at a given strength, as such inverse links are worked on and worked out.
However, all non-closepacked cubic steels - the body centred cubic ferritic steels, the body centred tetragonal martensitic steels and some of the precipitation hardening steels, have limited slip systems at ambient temperatures and higher diffusivities for hydrogen and as a result suffer to a lesser or greater degree from hydrogen embrittlement when subject to any operation that liberates monotomic hydrogen - such as acid bath plating or pickling cleaning. Below a YS of approximately 700MPa, there is little concern - the steel is usually plenty tough enough and ductile enough to survive such an event, but nonetheless good manufacturing practice is to give a specimen a 200 degree C bake for half an hour dependent on section to liberate any absorbed hydrogen. Above 700MPa, the material begins to exhibit greater and greater notch sensitivity for a given composition, treatment and grain size. All material at strength levels higher should be baked long enough to allow a half hour diffusion time per inch section at 200 degrees C. Any material tempered below 200 degrees C should *not* be allowed to be processed in a manner that liberates monoatomic hydrogen.
There ya go :-)