Reconstruction of the flag used by the German kings in the later medieval period (c. 12th to 14th centuries).
The existence of such a flag is certain for the 14th century, likely for the 13th century, and uncertain for the 12th century. 
It was used by emperor Henry VII in his Italian campaigns, and is repeatedly depicted in this context in Codex Balduini Trevirensis (c. 1340). In the Kassel Willehalm Codex (c. 1336), the same flag is (anachronistically) shown in a battle scene of Charlemagne.
According to Meyers Konversations-Lexikon of 1897 (s. v. "Banner"), the German Imperial Banner since the time of Sigismund (1430s), and "perhaps earlier" showed the Imperial Eagle, viz. a double-headed black eagle in a yellow field.

The banner used by some of the German kings or emperors of the late 12th and early 13th century may have shown an eagle, in the case of Otto IV an "eagle hovering over a dragon".
Image:Flag Germany Emperors Banner.png
Jaume Ollé; svg version by Masur