Rosch does list this unit on page 150, indicating it formed 12/39 and disbanded 7/40.
From Wikipedia:
The Flak Corps is a wartime organization, and constitutes an operational reserve of the commander in chief of the German Air Force. It combines great mobility with heavy fire power. It can be employed in conjunction with spearheads composed of armored and motorized forces, and with nonmotorized troops in forcing river crossings and attacking fortified positions. It can also be deployed as highly mobile artillery to support tank attacks
see also
http://www.ww2.dk/ground/hq/iflak.htm
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