According to Comic Book Legends Revealed #270, Namor the Submariner was the first in mid-1939.
In his very first appearance in mid-1939 in Marvel Comics #1 (which was actually his SECOND appearance, as he appeared earlier in the year in a giveaway comic that never was given away), Namor the Sub-Mariner flew!

He more explicitly flew in his next issue, Marvel Mystery Comics #2

These predate Captain Marvel's first flight in Whiz Comics #5 in June, 1940, and Superman didn't fly until 1941 in Superman #10 (and that was generally considered to be an art mistake as he didn't officially gain that power until later in 1943's Action Comics #65).