was he mentioned in any of plato's work?
Yes - in Plato's dialogue 'Timaeus'
Phaethon
In Plato's "Timaeus", Critias tells the story of Atlantis as recounted to Solon by an Egyptian priest, who prefaced the story by saying:"There have been, and will be again, many destructions of mankind arising out of many causes; the greatest have been brought about by the agencies of fire and water, and other lesser ones by innumerable other causes. There is a story that even you [Greeks] have preserved, that once upon a time, Phaethon, the son of Helios, having yoked the steeds in his father's chariot, because he was not able to drive them in the path of his father, burnt up all that was upon the earth, and was himself destroyed by a thunderbolt. Now, this has the form of a myth, but really signifies a declination of the bodies moving in the heavens around the earth, and a great conflagration of things upon the earth, which recurs after long intervals."
mention a few mythologies on planet? The Greeks made each planet sacred to one among their pantheon of gods, the Olympians: Helios and Selene were the names of both planets and gods; Phainon was sacred to Cronus, the Titan who fathered the Olympians; Phaethon was sacred to Zeus who is the entity mentioned at last who was sacred to zeus? Phaethon was the son of the Oceanid Clymene and the solar deity Helios in Greek mythology.
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Phaethon [SEP] Plato's "Timaeus"
In Plato's "Timaeus", Critias tells the story of Atlantis as recounted to Solon by an Egyptian priest, who prefaced the story by saying:"There have been, and will be again, many destructions of mankind arising out of many causes; the greatest have been brought about by the agencies of fire and water, and other lesser ones by innumerable other causes. There is a story that even you [Greeks] have preserved, that once upon a time, Phaethon, the son of Helios, having yoked the steeds in his father's chariot, because he was not able to drive them in the path of his father, burnt up all that was upon the earth, and was himself destroyed by a thunderbolt.