The flag of Athos with the double-eagle in the centre is a reminder of the old Byzantine flag. It shows the double-eagle, although in black on golden ground. It is really the symbol of Roman rule, which also survived in the flags of the Russian Czar, the Holy Roman Empire of the German Nation, or the Austria-Hungaryn Empire.
Source: Volker Preuß, Translator of the English text: Joachim Nuthack