Walkthrough

1. For completing this request, you can get Glide as a reward.
2. Waterside Dinghy Habitat Requirements and Spawns
3. Like any other move, Glide consumes PP. Make sure you have enough before following Dragonite to the other side.
4. Make a Waterside Dinghy habitat for Dragonite. You can do this at the top of the Pokémon Center Island, since there's already a canoe there. Power up your Leafage to spawn duckweed and complete the habitat.
5. Talk to Dragonite afterward, and it will teach you how to glide. By jumping and pressing R, you can now glide across the area and reach other islands.
6. Follow Dragonite again at the top to demonstrate the new move you learned. Cross to the other island to complete the quest.

Walkthrough source: Game8.