a quick brain dump, based on what i know.
with a target unit id, you can use
UnitAura(), and obtain the actual remaining duration of the aura(s) active on the target (presumably taking into account the caster's talents, etc). as far as i know, that is the "only way".
as far as i know, there is nothing simple/direct in the combat log, and even with a spell id from the combat log, querying via
GetSpellInfo(), there is nothing that can give you anything on aura effect duration.
i suppose you could try tracking matching sets of _AURA_APPLIED/_AURA_REMOVED events (match them up based on target GUID?), do arithmetic on the timestamps, and save the result per spell id for "future reference".