The flag you mention is the insigne of the Palaiologos who reigned from 1261 to 1453. As Dan Cernovodeanu pointed in his work, Eastern Roman (Byzantine) Empire did not use, or did not know, heraldry in the West European sense, but various aristocratics families had their personal symbols for use. During the Palaiologan period, the tetragrammic cross of the Palaiologos was the closest thing to a national flag.

The symbol is interpreted as the Greek letter beta, although it's also been interpreted as a firesteel, and the debate is still there. The two traditional readings of the four B would be translated as "King of Kings ruling over the kings/rules"

Sources:

Babuin, Andrea (2001) - Standards and Insignia of Byzantium

Cernovodeanu, Dan (1982) - Contributions à l'Étude de l'héraldique byzantine et post-byzantine