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This is the Air Service Command insignia. Repair of aircraft and processing of spare parts ordered by Material Command. Many squadrons under this command were assigned to groups in all theaters.
You could definitely use an AAC Headquarters shoulder patch and a CBI shoulder patch. Always best to find an image of a vintage jacket and copy it. These units were in all theaters and sometimes had their own squadron patches. My dad was in the 388th Bomb Group and the 434th Air Service Group was assigned to their Group/Base. However, I have never seen a jacket used by anyone from the 434th ASG and don't recall anyone coming to the reunions.
Probably a larger number of Air Service personnel at the Air Depots.