The Searing Demon Soul is obtained when defeating the Flamelurker boss. It cannot be traded for a spell or miracle so unless you really want those 18,000 souls, giving the Soul to Ed is the best option.
This allows you to use Boss Souls to create and/or upgrade unique weapons when talking to Ed.
Fun fact; the Searing Demon Soul originally was called Red Hot Demon's Soul in the PS3 version, so that might explain the lack on information on this online.