vulnerability

can anyone tell me what support gem I can use to get this to proc?

what about Mark on hit?

Vulnerability is a hex, not a mark, so mark on hit won't do it. (Hextouch is the closest hex equivalent.) Have a look at the wiki page for ideas of how to use it.

trying to incorporate vulnerability into this build which is proving difficult as SSF.

From my (limited) understanding Hextouch would need a supporting attack skill too?

Any idea how I can do so?

You link the hex and the hextouch support to a skill that hits (so it takes at least a 3-link) and then hit mobs with the skill, which curses them. But if you're low on links, it's probably easier to self-cast the hex, in which case it doesn't have to be linked to anything.

Another option is turning it into an aura with Blasphemy, but that takes two linked sockets and reserves mana.

would it work with damage taken support?

I could swap out molten shell (as not built correctly at the moment)

Sure, it just wouldn't be very consistent.