“In the second game Timothy subsided, though the fly hawk Hooper pulled down one clout from his cannon which had a very homerunny appearance.” Frederick G. Lieb, The Sun (New York), June 21. 1917, p13
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1927. “[Tris Speaker] can still make catches which it is believed no other flyhawk could negotiate, and throw strikes from the center field fence” (Paul W. Eaton, The Sporting News, Feb. 10; Peter Morris).