The flag's logo came from the east, when Phoenicians used the Phoenix bird in their legends, drawn to be a double-headed eagle which gives a new bird from its ash when burnt. The Byzantine Roman Empire (nation, state and culture) used it as its logo, as well as all nations that inherited the Roman culture as a logo for their kingdom or so.
The dual-heads refer to the dual civil and spiritual authorities in the Roman tradition, where the spiritual administration of the people was for the clerics, and the political one for the seculars, interactive and cooperative in one body. The two heads also refer to the ecumenism of the Christian vision, one is heading to the east and one to the west, while a crown with the cross is on the top of both heads.
The Phoenix bird is carrying a ball with a cross in its hand, the hand of spiritual authority, and a soward in the other hand, the hand of political authority, again both interact in one body, where every thing and every property is under the cross of the our Lord. The sword is the sword of justice and right, in which we stop the falsehood, hence maintain the word of justice and anti-evil, where our Lord Jesus Christ said: "And if you do not have a sword, sell your cloak and buy one" (Luke 22: 36), and "Do not assume that I have come to bring peace to the earth; I have not come to bring peace, but a sword (sword of the Gosbel)" (Matthew 10: 34). Yellow color refers to light and order.