The initial German solution to sending aid to Iraq was to run trains from Syria. Four trains loaded with munitions were sent to Iraq before "a few enterprising Frenchmen" blew up the "bridge near Tel Kotchek". That stopped further shipments by rail.
German reconniassance aircraft arrived in Syria in early May. They flew on Mosul on 11 May. The commander, Major Axel von Blomburg, was shot down and killed by mistake by Iraqi AA fire when he approached Baghdad at low level. The plan to send air aid to Iraq included 14 Me-110's and 7-He-111's from Fliegerkorps VIII. Some transports would also be sent. The Germans eventually suggested to the Italians that they send help, as well. Accordingly, 12-CR42 Falco fighters "arrived at Mosul on 27th May". By the time of Rashid Ali's exit from Iraq, the Axis had lost 14 Me-110s, 5 He-111s, and 3-CR42s.
This is based on the account in Vol.II of the Official History.