Megas Doux's flag
"and they, who are in the other (ships) as commanders ("kephalai") display the usual royal flag ("flamoulon"), which is the cross with fire steels ' but him, Megas Doux, the column of the king on horse"
( "και οι μεν εις τα έτερα (πλοία) ευρισκόμενοι άρχοντες ως κεφαλαί ιστώσι το σύνηθες βασιλικόν φλάμουλον ήτοι τον σταυρόν μετά πυρεκβόλων' ούτος δε ο μέγας δουξ την του βασιλέως στήλην ίστησιν έφιππον" )
-Pseudo-Codinos, De officialibus palati Constantinopolitani (Peri offikion)
Megas Doux was the General commander of the byzantine Navy since the 1080's.
His flag that in this passage is described, was similar to one of the "Royal Flags (flammoula)" as it is also mentioned in the same source.
The column with the emperor's equestrian statue was undoubtedly that of Justinian's in the Augoustaion main square of Constantinople.
It is described by various pilgrims and travelers and survived until short after 1453 and the Ottoman conquest of the city.
Justinian's statue on the column (left, contemporary drawing 1430 -right, modern representation)
the emperor in a ship with 5 flags (Skylitzes manuscript 12-13th cent)