I suddenly had a good idea.
I searched through the archives of Flight magazine, and I was shocked to discover many uses of the terms "angle of attack".
I was able to find the earliest use of this in print, which was in the November 6, 1909 issue.
There's a small article about some instruments available for "aeronauts":
A LEVEL AND WIND INDICATOR FOR FLYERS.—
The above photograph illustrates an interesting instrument which has been designed for use on flying machines by M. Arnoux, the Vice-President of the Technical Committee of the A.C.F. It indicates the force of the wind, the inclination of the machine, and the " angle of attack " when ascending or descending.
Fascinating! This term was being used at least as early as 1909. I'm curious, then, why most World War I era books used "angle of incidence" instead.