The name "Flying Fox" was used on three worlds, there was the Flying Fox of Earth-One who was a young Bruce Wayne and would later become that world's Batman. The Flying Fox of Earth-Two was a frequent foe of sky criminal Air Pirate A-X. The Flying Fox of the Post Crisis Earth seems to have originated on Earth-X previously.
Darrell as a flying detective in the image of his world's Batman paralleled that of his counterpart, Kirk Langstrom who was also a private investigator with the ability to defy gravity. For Kirk, it was when he studied the nocturnal gliders that the Dark Knight was modeled after, and developed a bat extract. With this chemical compound, he became the inhuman Man-Bat of Earth-One and was a hero and villain.
There were other creatures on their respective worlds. On Earth-One, there was Andrew Bennett, Lady Viper, Anthony Lupus and Gregori Arcane who each mirrored Earth-Two's Creature Commandos in Vincent Velcro, Myrna Rhodes, Warren Griffith and Elliott Taylor. While the former quartet each interacted with the Batman on their Earth, there is no documented occurrence of the later foursome having met their own Batman, since they operated primarily in Europe during World War II before the were jettisoned into space accidentally on a last mission.
Additionally, in both Batmen's Gotham City, there were other caped crusaders that protected these modern metropolis' from the shadows. On Earth-One, it was Jason Blood whose Etrigan alter ego aided by Glenda Mark and Harry Matthews assisting in bringing justice to others
On Earth-Two, it was Justin Arthur who like Blood was a time lost warrior from ancient Camelot, who was aided by Eve Barclay and Doctor Moresby in his adventures. While not a creature himself like Man-Bat or Etrigan, Justin had his flying steed Winged Victory always by his side.