Holy Roman Empire
In this TL, the flag of the Holy Roman Empire went through a number of changes during the unification process led by the Kingdom of Burgundy between 700-1000. The first Burgundian flags were simple red and blue war banners, where both red cross on blue and blue cross on red were used. With the conquest of Kingdom of Aquitaine, the design was consolidated to a red cross on a blue field with a red border, fimbriated with white. The arms of Burgundy and Aquitaine were quartered on the flag.
This design was to last for more than a century. However, the conquests of Neustrasia, Austrasia and Westrisia in a quick succession added yet more arms to the flag. Then, instead of quartering the arms yet again, it was decided that each field shall bear the separate arms of all four kingdoms, with the arms of Burgundy in an escutcheon above them in the center. This design was to last until Lothere the Pious of Burgundy, the first Emperor.
It is said that after the conquest of Kingdom of the Lombards and the coronation in Rome, Emperor Lothere had an epiphany that made him devote his empire to the glory of God. This had profound impact to his entire reign, but also to his arms and the Imperial banner as a result.
Lothere ordered to clear his arms of all designs accumulated over the previous centuries, leaving only the red cross on blue field, bordered by red and bearing an escutcheon. To this, he added the papal cross, stating: "Only the arms of the Most High should stand above all." This would become the Imperial Banner for centuries to come.
Kingdom of Aquitaine
In this TL, the Kingdom of Aquitaine was dominated by the Basques. Their war banners were originally green and red, often bearing the Basque cross. Before Emperor Lothere, the Aquitaine arms stood in the upper left field of the Imperial banner, bearing the red Basque cross on white.
The banner for the Kingdom alone, after Emperor Lothere, became a field quartered between Burgundian blue and Basque green, bordered by red to recall their position on the original Imperial banner. In the center stands the ancient Basque cross in red, on a white roundel.