How to Catch The Flying Gyarados in Pokémon Legends: Arceus 

In order to capture a pokemon, it may take a few tries to catch it. To do this, you will need to collect many Apricons and sky tumblestones to make 20 or more feather balls.

Location: Northeast of Deertrack Heights and across Obsidian falls.

Adjust your position to be in the right place at the right time.

You may need to take some time to adjust. Maybe try a few soft balls to begin with, because you may have a tough time spotting this rare Pokémon.

Point your crosshair at the path of your target.

In this case, having a feather ball would be better than a regular Pokeball. A feather ball has a longer range and a more accurate trajectory, so it would be more effective.

If a Pokémon flees, it could create a roar, and then continue to fly. You need to use this to your advantage.

If a Pokemon avoids your first special attack, hold down ZR and release it to throw another one.

You'll catch them mid-roar, unable to move, and you'll keep repeating until you get your flying Gyarados.

If you want to reproduce, there are three ways to do so. You can wait, rest, or leave the area and return to Jubilife City.

When catching Gyarados, another one will quickly take its place.