Well, before the Time Crash the Frozen Flame was first rumored to be in the hands of Guardia, as RD shows. But, regarding just CC, no idea, could be as how RD states it, but anyway, it then came into hands of Chronopolis.
Afterwards with the whole being sent to the past thing, it could be that after the terraforming and memory wiping, the Frozen Flame became part of the flavor of whatever setting was planned beforehand for El Nido. Perhaps...