So based on author's description, I just tried to do the flags of the countries of TAS world.
So this was author's description of Carthya's flag: The Carthyan flag has three gold stripes across the upper third. In the center of the flag is the king coat of arms. The Carthyan crest is in the shape of a blue shield with a gold stripe running horizontally to divide the upper third. The right side of the stripe bears an image of the king’s ring, and the left has a knot. The uppermost of the crest is held by a falcon, The bottom third has a griffin bearing a laurel around its neck. A bottom banner lists the words "Egolath & Corodir", meaning Duty and Honor.
So I think Carthyan flag looks like this perhaps based on the description.
And Bymar's flag's description was: Bymar's colors are blue and white. The flag is divided into four squares, blue and white on the top and white and blue on the bottom.
So Bymar's Flag
And Mendenwal's flag was said to be like this: The colors of Mendenwal are yellow and white. Mendenwal's flag is white with three yellow stars in row in the center.
Probably Mendenwal's flag is like this
And Gelyn's flag was said to be like this: Gelyn's colors are yellow and green, the flag of Gelyn is yellow with a green rectangle in the upper right corner.
Gelyn's Flag could be like this
And Avenia's flag description was like this: Avenia's flag is entirely red with the black emblem of the pirates at the center, to acknowledge them. And we know pirate symbol is an X with a sea serpent angled northeast and snake angled to north west. ( I couldn't do that very well but it is mostly like this. I don't know if it's correct. I took direction of the heads)
