The Solar Flux won't work that great if you need to weld a subsequent pass, including any "touch up" weld pass. When it cools, parts of it can crack and "pop" away as the metal contracts, so it will not reliably protect the metal on any subsequent welding passes or "touch up" work. However it might be a good alternative to purging a very long, relatively large diameter exhaust system (saving you lots of effort getting a large volume purged.)
For tungsten diameter, I would go .040" or "sharp" 1/16" for better arc starts and low-current arc stability. For filler rod size I would go with 1/16, not the 3/32" unless you have some really big gap from really poor fitup you are trying to bridge (and definitely back purge if you are doing that, or better yet, try to avoid it.) You might even try to locate a filler rod smaller than 1/16". (I've got some 3/64")
I like using 309L for most of my stainless welding.
Attached picture is a stainless steel chair .049" diameter, I welded using 1/16" 309L and .040" tungsten. You don't want to use much amperage for welding stainless. I usually control with footpedal, but would guesstimate about 40 amps average or less for exhaust tubing. Keep a tight arc to focus the heat and make a narrow puddle, and minimize overall heat input. Weld in stitches and allow cooling of the part in between. If a large portion is glowing red after you are done welding a stitch, take a break and do something else to allow the work to cool before welding near there again. Stainless is slow cooling. A larger diameter gas lens cup is also adviseable. Using some pulsing to minimize heat input if your machine offers it. (For this I would go with min. pulse freq, min. pulse duty cycle, and minimum background current.)
Oh and almost forgot, use plenty of post-flow to keep the metal shielded, it needs to stay shielded with argon even a little bit longer after it stops glowing. You can re-trigger the post flow by tapping on your footpedal, repeatedly as many times as is needed. Avoid the "dull grey" looking heavily oxidized surface.
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