You can't get the cooldown of another players spells or items with the WoW API, so you would have to either implement some sort of addon communication in your aura and have them run it too, or find another addon that implemented that.
You can watch for, eg, spells cast by them, or buffs on them, and make guesses about how long things last. That is: you can't track the skull banner cooldown, but you can observe that skull banner was cast, and show something for 60 seconds (or whatever the cooldown is) to let you know when it is back up. As long as nothing resets their SB cooldown, that could work.