The 1938 version of Superman did not fly; Superman did not fly until some time in the 1940s. Earlier Western stories, based on Theosophy, had portrayed "the astral plane" as medium for non-physical "flight" as early as 1886.
Many Western stories represent a flying "point of view" in the sense of a disembodied dream or visionary experience.
By the 1930s, there were superheroes with the power of physical flight.
However, one of the most powerful comic book heroes predating Superman was Mandrake the Magician (1934),who had almost any power the writer (Lee Falk) cared to grant him.
Did Mandrake ever demonstrate the power to fly or levitate prior to Superman's first flight?