Vitriolic Blast deals additional 2d6 acid damage in rounds after the blast. Would a Chasuble of Fell Power apply the extra d6 damage to those rounds as well?
Also, looking at the brimstone blast it states that multiple hits do not increase the damage per round. So if you're hit by a fiery blast you get a static 2d6 fire damage from burning. So I would say that the vitiriolic blast would be the same, adding to the initial damage but not lingering effects of the acid.
Though I suppose there is an argument to be that vitiriolic blast is a greater invocation and brimstone is only a lesser invocation.
vitriolic blast's effect is not eldritch blast, its a residual effect from being hit by the blast, so the chasuble doesn't increase the 2d6.
however, each hit from vitriolic will put a 2d6 dot on the target for the listed number of rounds, unlike brimstone blast which specifically says only one dot can be placed on it; vitriolic lacks this wording.
OP: No. Additional dmg like that never(?) applies to "DoT" dmg. If anything it would only apply on Round 1. I do not have a rules backing for that in mind at this time... might even be a House Rule. I'll get back to you later.
Consider (if you DM allows) Empower SLA, Boost SLA, Quicken SLA and Mortalbane all from BoVD...