This straight black cross, often called the "Balkenkreuz," was a World War I insignia adopted by the German Air Service in mid-April 1918. Variations of the straight cross design replaced the earlier "cross pattée" insignia on all German aircraft for the duration of the conflict and beyond.
This particular burlap fabric was removed from a decoy/dummy aircraft used by German gunners to try and lure Allied aircraft into range of their anti-aircraft guns.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.