Although today it is believed the flag that the Church of Greece presently uses was the flag of the Byzantine Empire, there is no proof. The double-headed eagle that looks on the east and the west on a yellow background is indeed the symbol of the Greek Orthodox Church, and you will see it outside many monasteries and churches. However, there is no sign of how it was created.
Some believe that this eagle represents the strength of the Byzantine Empire that extended from the east to the west and that the Church uses it today to remind the pilgrims of the strong influence that is used to exercise during the Byzantine Times, which means that it used it as a sign of power and glory.
The flags you will frequently see today in Greece are the flag with stripes and the double-headed eagle. The flag with the cross in the middle is no longer used, and you will find it only in museums.
The Greek National Flag celebrates October 27th, a day before the Greek National Holiday for the resistance in the Second World War, when the Italian troops invaded the country in 1940.