I’ve looked into this and have had a very difficult time attesting any really consistent motifs for imperial heraldry until the Palaiologos and the 14th century. The idea of families or dynasties having official insignia was not really introduced until the Late Medieval Period, and so there was no standard image for the imperial families.
This article by Dr. George Theotokis on Medievalists.com discusses it at length. The double-headed eagle motif came into use around the mid 12th to early 13th centuries and was used increasingly after that, but there’s really no evidence of it being an official flag/symbol/motif until the Palaiologai adopted it as heraldry in the western fashion.
Before that, symbols were largely personal. A labarum standard was apparently not rare. Christian imagery including the cross or the Virgin Mary would not be uncommon. Apparently a single-headed eagle style was in use up through the 11th century and beyond, but I’m having a hard time finding pictures. Military units in the Madrid Skylitzes are depicted with banners like this one below
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At first, I assumed these to be simple unit standards with no real imperial significance but..
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The color scheme seems to be in use immediately around the Emperor Theophilos both as a standard and on the imperial throne. Perhaps there is more to that.
The coinage of the middle Byzantine period has many crosses and some depictions of angels or Jesus along with the reigning emperor(s), but nothing of the eagles or the Chi-Rho people traditionally show as Byzantine insignia.
It’s very hard to draw flags and imagery for them as we would like to because half the time we don’t know and the other half of the time we are just projecting understandings of western insignia onto the empire. You may find something if you check out Constantine Porphyrogennitos’ Book of Ceremonies. It just occurred to me to email a specialist on this and see what they can say, so I’ll try and do that today and post responses.