As to how Fate could have done it. I think Fate might have still been partially active in Home World..but then again I'm not entirely sure.
It was probably FATE, or at least "the Fates". The 3 flaming stuff which appear and destroy the Dead Sea come from the same spot where the Fates statues (Clotho, Lachesis, Atropos) are located in Another World. These spots are named "Fate distortions" and Serge use them to go to Another Sea of Eden.
I like that, because it fits perfectly in with my other theory of how Fate could destroy the Dead Sea from another dimension if Fate had some control over the other three dragons in that same dimension while Fate is in a separate dimension.
I also think that Clotho, Lachesis, and Atropos are all controlled by Fate. Remember how the magnetic storm temporarily shuts down Fate which caused Chronopolis' defenses to open, which allowed Wazuki, Serge, and Miguel entrence to Chronopolis? Well, exactly what defenses were there to be that would block entrence to Chronopolis? I think that, that defense was the Fates statues; Clotho, Lachesis, and Atropos which are controlled by Fate itself since Fate pretty much controls all of Chronopolis. When the magnetic storm ebbs away, Fate comes back online and the defenses go back up. Clotho, Lachesis, and Atropos which are those same defenses of Chronopolis, come back up since Fate was online again. Also note that when you defeat Clotho, Lachesis, and Atropos, that you opened up Chronopolis' defenses once again since you couldn't access Chronopolis before defeating Clotho, Lachesis, and Atropos. Fate's defenses were defeated which allowed you access to Chronopolis. That magnetic storm just temporarily shut Fate down which is the source of Clotho, Lachesis, and Atropos, which is the defense, which were the defenses that were also left opened temporarily.
Now, with that theory said, I can fit it perfectly into how Fate was able to destroy the Dead Sea.
Assuming that my above stated theory is correct about Clotho, Lachesis, and Atropos being controlled by Fate, and having Fate being able to influence the destruction of something that is in a separate dimension since Fate is obviously influencing control over three of the six dragons that are also in a separate dimension; Fate used Clotho, Lachesis, and Atropos to destroy the Dead Sea since as you stated, Chrono '99, the three flaming stuff that was used for the Dead Sea's destruction, came from the same locations as Clotho, Lachesis, and Atropos. They were able to use those distortions that Serge later uses to reach Chronopolis, to destroy the Dead Sea from.
Now with that said, we can also assume that it
was indeed Fate who destroyed the Dead Sea, and that it
was indeed Fate who said, "I love you so much. That is why I sometimes desire to smash you to bits!!!"
I think there was only one Frozen Flame but if there were two, Fate probably destroyed the Dead Sea to also destroy the Frozen Flame in Home World, and to destroy Serge. But, if there is only one Frozen Flame, then Fate destroyed the Dead Sea to try and destroy Serge. I don't need to point out any further evidence of why Fate would want to destroy Serge since I'm sure you all know why.