Exactly, the flame champion died in the cave where he lived with his girl. So it is pretty much impossible for Kai to be the flame champion, unless for some odd reason the flame champion didn't die and Konami has been yanking our chin. I will vote that he actually died in the cave, evidence points to this when the destroyers broke into the cave and was repelled back by the supposed spirit of the flame champion. This may end up in the unjustifiable section.
EDIT: A bit more evidence, The Flame Champion was born in SY 390 in the Grasslands, he died SY 475 of natural causes in the Grasslands. As for Kai he was born in the year SY 408, he hasn't been pronounce dead.
Sandalphon - Senso Suikoden