Having served with the 2nd Guards Uhlan Regiment and the 4th Guards Foot Regiment, Barnekow joined the Luftstreitkräfte in February 1917. After gaining experience as a two-seater pilot with FEA 5, he was posted to Jasta 4 in September 1917. Here he served with Ernst Udet under Kurt-Bertram von Döring. On 10 March 1918, Barnekow was posted to Jasta 20 and scored his first victory two months later, downing an S.E.5a piloted by Henry Dolan of 74 Squadron. Barnekow claimed 3 more victories before he was wounded in action on 23 August 1918. In September, he returned to duty with Jasta 20 and scored 1 more victory before being reassigned to Jasta 1. With this unit, Barnekow was wounded in action on 2 October 1918 and scored 6 more victories by the end of the war. During World War II, he served on General von Doring's staff and in 1941, shortly after the death of his friend Udet, Barnekow also committed suicide.