Hi John,
you assumed correctly. Albeit in the time frame you mentioned the unit was officially called "Flieger-Regiment 32" (
http://ww2.dk/ground/infanterie/flausb32.html). 3./Flg.Rgt.32 (in arab numerals) should mean "3. Kompanie", so first battalion.
Those units basically provided infantry training for Luftwaffe soldiers while also guarding important installations.
Cheers,
Christian