The king of this country is not a person, but a divine beast with three pairs of wings, said to dwell far up in the heavens.
Literal
This country [gen-の] king [topic-は] person [copula-ではなく], far heavens [in-に] honorific-dwell [quotative-という] three-pairs [gen-の] wings [obj-を] possess divine-beast [copula-なんだ].
神獣 'divine beast' is a fantasy/mythological compound. 三対の翼 'three pairs of wings' uses the counter 対 for matched pairs. 居られる uses the honorific passive on 居る — even a beast, if it's a king, gets elevated language. ~という packages the preceding clause ('said to dwell in the heavens') as a defining attribute of the noun that follows.