Armenian historians have reconstructed the coat of arms of the Mamikonyan dynasty to look like this: a double-headed eagle holding an animal in its claws. The coat of arms was reconstructed relying on sculptures in ancient churches. The oldest picture is known to be the one on the façade of the church if the village of Dsegh (VII century). The flag of the Mamikonyans is mentioned in the “History of Armenia” by Pavstos Byuzand (V century).

Old Armenian is hard to be translated and it is considered that the “History…” describes a flag depicting an eagle holding a bow. The color was reconstructed to be red (the same “History…” describes that the Shah of Iran sent the heir to the throne a red marquee). The pictures in the church of Dsegh and others may just as well be of decorative nature.

Undoubtedly, the medieval state of Cilicia also had its flags. They are usually reconstructed as purple color cloth bearing crosses. The reconstruction is probable but not trustworthy. Actually, Armenia has made Christianity its national religion since 301 but no pictures of these flags have been preserved.

Descriptions of the royal flag of the Luzinyan dynasty (XIV) century: white-red-blue-yellow. Some Armenian historians are inclined to believe that the white is the color of the dynasty itself, and the remaining three are national colors of Armenia.

During the reign of Tigran the Great (95-56 BC), the dragon with seven was the coat of arms of Armenia.

During the reign of the Arshakuni Dynasty (62-428 AD)a new coat of arms was adopted: a single-headed eagle holding a snake in the beak. I wasn’t able to find a picture. This is what I can offer as an illustration.
The flag of the Artashessyan Dynasty (2-1 BC)

This is to commemorate Soghomon Tehleryan in Canada; during my last visit I happened to see an identical monument on the way from Yerevan to Hrazdan.

Site  Armenian Heritage has its own version:

Armenian Heritage

It was the end of the fourth and beginning of the seventh when Armenia was mainly under the Persian control, and its minor part under the Byzantine Empire. The Persian part was referred to as Perso-Armenia. Then the Persians were trying to establish pyrolatry in already Christian Armenia. Several religious wars and battles occurred. The most famous of them was that of the Vardanank – the battle of Armenians and Christians of the Caucasus (Iberians and Albanians) under the flag of the Mamikonyans against Persia. This is when the Christian cross became a major form of identification and confrontation to the occupant.

Flags of the Mamikonyan Dynasty (4-9 centuries) that was one of the most famous princes of Armenia, in the Middle Ages perhaps became the most significant one.

A two-headed eagle holding an animal in the claws. In another version the eagle holds an arrow.

In the 9th century, when Armenia regained its independence, the Bagratunis became dominant. The flag of the Bagratunis remained the flag of Armenia until the 11th century.