You can start by looking on fanfiction websites like FanFiction.net or Archive of Our Own (AO3). These platforms have a wide variety of Pokemon fanfics, including ones featuring Ash and Dratini. Just use the search function and type in relevant keywords like 'Pokemon Ash Dratini' and you should be able to find some interesting reads.
One great 'Pokemon Ash and Dratini' fanfic could be about Ash finding a Dratini in an unexpected place, like a hidden cave. The fanfic might focus on Ash's determination to train it and form a strong bond. It could also include Dratini evolving into Dragonair as they face challenges together.
It could be a legendary Pokémon in disguise. Legendary Pokémon sometimes interact with trainers in mysterious ways. This one could have chosen Ash to receive the Dratini egg as part of some grand plan to help Ash become an even greater trainer and perhaps save the Pokémon world from a future threat.
Dratini's character could be developed by showing its initial shyness. Since it's a relatively rare and often timid Pokemon, it might be scared of Ash at first. But as Ash shows kindness, Dratini could start to open up. Maybe it would show its playfulness when it gets more comfortable around Ash and the other Pokemon in his team.
The plot might involve Ash's Dratini evolving quickly due to their unique connection. It could also have elements of Ash trying to prove that Dratini can be a very powerful Pokémon from the start. He might enter it into Pokémon contests and battles, showing off its unique moves and abilities.
In the fanfiction, perhaps Ash catches Dratini during a quest. He hears rumors about a rare Dratini in a certain area. He goes there and finds Dratini being chased by some other Pokemon. Ash steps in to protect it and earns Dratini's trust. The story could then focus on their adventures together, exploring new regions and facing tough opponents with Dratini by his side.
One popular story could be about Ash and Dratini's adventure in an uncharted forest. They might encounter rare Pokémon and have to work together to overcome challenges. In this story, Dratini could start evolving during a tough battle, which adds an exciting element.
There are many great authors. Some might be known within specific fanfiction communities. One author could be someone who goes by the username 'PokeFan123'. Their stories often focus on the emotional bond between Ash and Dratini, and they write in a very engaging style.
His friends like Pikachu for sure. Pikachu would be there by Ash's side, probably as curious as Ash about the Dratini egg. Brock might also be involved. He could use his knowledge of Pokémon to give Ash some tips on taking care of the egg.
Ash would likely become more responsible. Since Dratini is a relatively rare and potentially powerful Pokémon, he'd have to take extra care. This could make him think more before acting in battles and other situations.