It does look and feel scary, but it doesn't melt or harm the line as far as I know.
I have vinyl tubes soaking in Starsan perpetually. They do get slick after a few days, and turn cloudy after longer immersion. It could be some plasticizer in the PVC reacting with one or more ingredients in Starsan, which contains phosphoric acid, dodecylbenzenesulfonic acid, a surfactant, and a small amount of Sodium EDTA, a strong cationic sequester.
Just drain the Starsan and they will be fine. If they've turned cloudy, drying for a few days will make them crystal clear again.
You could pump (recirculate) some PBW water through them to rinse out the slimy residue, rinse with water and resanitize with Starsan but not for 3 days. A few minutes contact time is sufficient. Even an hour won't turn them slimy.
[...] I have noticed that it can make flare fittings corrode to a pretty blackish color [...]
Flare fittings are not stainless, I found that out too, they are a brass alloy, and the chrome plating turns black from the acids in Starsan. It brushes off and you'll end up with a dull brass fitting. Lesson learned: don't soak them in Starsan for prolonged time. 1-2 minutes contact time is enough.