Okay, imo :
It was said in the anime that Iris and Diantha are champions, but not said in the anime that Kukui is champion or something, I mean, the games argument isnt very convincing considering that Acerola, Kahilli And the girl with the fairy-type Pokémon are bad trainers in the anime.
Kukui doesn't have a title to back him up, Incineroar doesn't have an achievement to back him up, and there's no way to show how much power Melmetal has, he fought very well against Silvally, but Tortunator did very well too, Incineroar beat him very easily, but speaking of Flint, his Infernape also defeated Ash's Infernape very easily, and with no type advantage, and Ash's Infernape> Melmetal..
Sure, he (Incineroar) defeated a Mega with Z-Move, but it was a TR guy we don't know how strong he is.
In conclusion, there is no way to prove that Kukui is champion level imo, Although it is fine if you believe it, after all he is the strongest trainef in alola.