I'm kind of confused what year akatsuki no yona is set in because in the manga, Zeno claims to be more than 2000 years old, so shouldn't it be year 2000 or something around that? even though it looks like it's been set way way WAY before that...
The answer can be found from here, Why do the characters in Akatsuki no Yona have Korean names?
The setting for Akatsuki no Yona is loosely based on the Three Kingdoms of Korea period. The Kouka Kingdom is inspired by the Goguryeo Kingdom. Its neighbor Sei and Xing are based on Baekje and Silla respectively. You can also see that the three kingdoms are located in a peninsula in the manga and that they almost have the same layout as their real-life counterparts.
From the wikipedia article,
The concept of the Three Kingdoms of Korea (Hangul: 삼국시대; Hanja: 三國時代) refers to the three kingdoms of Baekje (百濟), Silla (新羅) and Goguryeo (高句麗), which was later known as Goryeo (高麗), from which the name Korea is derived. The Three Kingdoms period was defined as being from 57 BC to 668 AD
Thus its safe to say from the setting and inspiration that Akatsuki no Yona, may be from a similar time period, where obviously dragons exist.