I can't remember a definite year for when I read it, or when it was published, other than that it was between 3-8 years ago. I originally found the story on fanfiction.net.
In the story, Harry discovers he can do magic, learns to fly based off of Peter Pan as well as some other tricks like shrinking and enlarging things, and leaves the Dursleys. After that, he travels around, learns more about magic, and there's a lot of world-building. One of the incidents I remember is when he gets caught by some spider being and makes a bet with it to get his freedom. Another one is where he accidentally finds a dormant god and wakes them by kissing them, like how Snow White and Sleeping Beauty were awoken. There's also a giant robotic penguin made by some mad genius wizard that's obsessed with penguins.