Ash first encountered Dragonite as a Dragonair on Dragonite Island in JN010. Unlike the other Dragonair on its home island, it had trouble learning how to fly. Seeing this, Ash offered to help Dragonair learn Dragon Dance and master the use of its wings. Using an Electroweb trampoline provided by Pikachu, Ash managed to help Dragonair to overcome its shortcomings.
Dragonair then sensed Team Rocket capturing one of its Dragonite friends, and the group intervened. Team Rocket sent out a Wailord to deal with them, and one of its splashes sent Ash flying into the air. Dragonair tried to save him from his fall, but its skin was too slippery for Ash to hold on to. As such, it then proceeded to evolve into Dragonite and save Ash. After Team Rocket was defeated, Dragonite expressed its willingness to come with Ash, and he caught it.
Much like Ash's Muk, Dragonite has a habit of embracing people and Pokémon, even when meeting them for the first time. In JN021, it even tried to hug an unhatched Egg, forcing Ash to tell it that it shouldn't do so. It also displayed both courage and determination in saving Ash, which gave it the boost it needed to evolve. It cares for its friends, as it didn't hesitate to come to the aid of its Dragonite friend and for Ash.
Like many of its species, Ash's Dragonite is an adept flyer, and relishes the chance to do so. In JN014, Ash used Dragonite to help him and Pikachu cross the Desert Resort, and was happy to race with Goh and his Beedrill to see who was faster, becoming so engrossed in the race that it sent Ash and Pikachu flying through the air. Dragonite was overjoyed by its victory, and while it obediently returned to its Poké Ball before Ash and Go entered the cramped Ruins of the Titan, it was visibly disappointed.