Kirkpatrick's book (Archie in the A.E.F.: The Creation of the Antiaircraft Service of the United States Army, 1917-1918) indicates there were two numbered Anti-aircraft Artillery Battalions in the AEF Nov 1918 (1st AAA Bn with First Army, 2nd AAA Bn with Second Army), each with four lettered firing batteries (A, B, C, and D) that were permanently assigned to the battalion. In addition, the HQ of the Anti-aircraft Artillery Service of the A.E.F. had three numbered (battalion-size) "A.A. Sectors" (each with four or more numbered A.A. firing batteries) -- the 8th A.A. Sector, 9th A.A. Sector, and 10th A.A. Sector. The A.A.A. School had eight additional numbered (battalion-size) "A.A. Sectors" -- the 3rd, 4th, 5th, 6th, 7th, 11th, 12th, and 13th A.A. Sectors -- each with four or more numbered A.A. firing batteries. Kirkpatrick wrote that the numbered A.A. firing batteries were not permanently assigned to any A.A. Sector, but were task organized depending on the mission. All of these Anti-aircraft artillery units were formed from the Coast Artillery Corps (though the majority of men actually were French soldiers -- about 1,000 U.S. troops versus about 2,400 French troops in the AAS).
There were also six numbered A.A. machine-gun battalions, which were manned by the Infantry. 1st A.A. MG Bn was assigned to the Second American Army, 2nd A.A. MG Bn was assigned to the American First Army, and the 3rd, 4th, 5th, and 141st A.A. MG Bns fell under the AAA School.
Finally, the Anti-Aircraft Artillery Service of the A.E.F. included the 56th Engineer Regiment (Searchlight), which had 10 searchlight companies, each with 5 platoons. These platoons were task organized under the A.A. Sectors or assigned to the Chief of the A.A. Service of the First or Second Armies.
I think the patches you are showing are those of the Anti-Aircraft Service of the A.E.F., rather than a distinctive patch for an individual battalion or battery. That would explain the Engineer letter "E" below one of the patches. And it would explain why someone who served in the 5th A.A. battery (or the 5th A.A. Sector or the 5th A.A. MG battalion) could say it was the patch they wore.
Per the CMH 60-16-1 Organizational History of the Field Artillery, a January 1918 modification of the TOE added 12 anti-aircraft artillery guns to each FA Regiment (in addition to the existing anti-aircraft machineguns).
Per the CMH 60-5 (Air Defense Artillery) provides the lineages of all ADA units in the Army -- but only mentions the 1st Anti-aircraft Artillery Battalion from WWI.
Kirkpatrick's assertion about there being only two numbered AAA Battalions in the A.E.F. is contradicted by the Biographical Register of Graduates of the US Military Academy (vol 6), which lists several officers who were assigned to (including serving as commanders of) the 1st, 2nd, 3rd, 4th, 5th, 6th, and 7th Antiaircraft Artillery Battalions in France during WWI. These were MAJ Gooding Packard (1st AAA Bn), MAJ Harry A. Schwabe and MAJ Ira A Crump (both commanding 2nd AAA Bn at different times), CAPT Joel G. Holmes (Adjutant, 4th AAA Bn), MAJ Charles R. Finley (5th AAA Bn), MAJ Bird S. Du Bois (6th AAA Bn), and MAJ Christain G. Foltz (7th AAA Bn)
Has anyone discovered any additional Anti-Aircraft shoulder insignia from WWI (e.g., is there a different patch for the 1st AA Bn, 2nd AA Bn, 1st AA MG Bn, 56th Engineer Regiment (Searchlight), etc.)? The only other shoulder insignia I've seen is a First Army "A" with the letters "AA" at the bottom and the number "5" in the upper opening.