The only obvious reason why King and Urouge wings are bigger than the on of a normal Birkan is because of their sizes. Urouge is already big enough as the size of a pacifista and King is comparably the size of Queen. The bigger the body, the bigger than wings need to be so they can fly. Normal size Birkans, like Ohm, have normal size wings.
Normal Size Wings Tenguyama's is already a big man, so because of that his wings are extremely big. https://vignette.wikia.nocookie.net/onepiece/images/1/13/Tenguyama_Hitetsu_Manga_Infobox.png/revision/latest?cb=20190223222504&path-prefix=es
The wings' size depends on the person's weight and height. Again, this is a theory, so it's possible the King and Tenguyama are indeed from different race which Urogue is not from.
Not that the Anime is anything for canon size measurements, but Tengu appears to be approximately Luffy's height without the Geta Sandals.
I can see King being some "Phoenix" version of the Birkans with some un-introduced properties that make his race so rare in the present. His hair is literal fire.