Operating from Chièvres Air Base from 27 May 1940, Müncheberg claimed his fifth aerial victory over a Supermarine Spitfire on 29 May 1940. This achievement earned him the Iron Cross 1st Class (). At the time, III. "Gruppe" was providing fighter escort for Junkers Ju 87 "Stuka" dive bombers and Messerschmitt Bf 110 heavy fighters operating against the beachhead held by British Expeditionary Force (BEF) in the Battle of Dunkirk. Fighter Command recorded the loss of 10 fighters to Bf 109s on 29 May. On 31 May, Müncheberg claimed an unprecedented four Spitfires over Dunkirk, as the evacuation and battle of the port reached a climax. The last claim of the day was made against No. 609 Squadron. No. 609 Squadron reported two pilots killed and one wounded, though one of the dead pilots was killed in action with Heinkel He 111 bombers according to British sources.