Flag explanation from the source site (written down as it was displayed within the flag image):
Approved Indigenous Symbolism
Antiochian Greek - Levantine Rûm Flag
Yellow (Gold)
Taken from the standard of the Palaiologoi; the last ruling dynastasy [sic] of the Eastern Romaic Empire. It symbolizes the Levant's Romaic heritage.
Purple
Symbolizes the Phoenician heritage of the region; whose Civilization was the result of a blending between local Canaanite peoples & the Hellenic Sea Peoples.
Red
Taken from the standard of the Palaiologoi; the last ruling dynasty of the Eastern Romaic Empire. It symbolizes Martyrs of Antiochian Hellenism.
The emblem in the center is an adaptation of the Romaic Two-headed Eagle. The laurel wreath, which surrounds the Eagle represents Hellenic Civilization. While the Anchor on the Eagle's chest represents the Levant's Hellenistic heritage. The Anchor was the symbol of Seleucid power, and was placed on Seleucid coinage. Tomislav Todorović, 30 December 2022
Antiochian Greek Christians (also known as Antiochian Rum) are a Levantine Arabic-speaking ethnoreligious Eastern Christian group residing in the Levant region. The highest concentration of Antiochian Greek Christians still living in the Levant are found within the territories of Syria, Lebanon, and Turkey. Counting the worldwide diaspora, there are more than 1.5 million Antiochian Greek Orthodox and Greek Catholic (Melkite) Christians residing in the northern Middle East-North Africa region, the United States, Canada, Australia, and Latin America today. Alexandros Katechis, 28 December 2022