It's the Flak crew sleeve patch. The entry says:
Tätigkeitsabzeichen d. [= der] Flakart. [= Flakartlilerie]. Battr.Bef. [= Batteriebefehl] Nr. 21
Oblt. [= Oberleutnant] u. [= und] Batterieführer"
"Trade Badge of the Anti-Aircraft Artillery. Battery Order no. 21
Oberleutnant and Battery Commander"
Thanks HPL! I looked through every badge and clasp I could find for a similar looking match, and never would have thought to look for a patch. This is the first time I've come across one listed. Quite interesting.
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