Flamadin is some sorta undead abomination and doesn't even have a soul, and was in conflict with John. Though they were also fused together at some parts, and each one was struggling for control. However, it's from that we know that the soul of an Eternal Champion is distinct from their actual identity or personality. It merely acts as a vessel for it. It makes the fact that Elric's daughter and son are also Eternal Champions a lot less weird. They also don't inherit Elric's memories of him fucking their mother. Which would have been funny, but it didn't happen. Thank goodness.