One possible reason could be that they are framed for a crime they didn't commit. Maybe some powerful and malicious forces within Konoha set them up to take the blame for something big, like a failed mission that was actually sabotaged by others.
In the midst of the flee, they could also have some arguments. Maybe about the direction they should take or the methods to avoid being caught. But these arguments could actually lead to a better understanding of each other in the end. For instance, after a big argument, they realize that they both have the same goal of survival and protecting the village in the long run, which deepens their relationship.
One possible plotline could be Naruto fleeing due to false accusations. Maybe he's framed for a crime he didn't commit and has to run to clear his name. Another could be that he discovers a dark secret about Konoha and decides to leave to avoid being part of it.
Obviously Naruto himself is the main character as the story is about him fleeing Konoha. Sasuke could also be involved. He might be the reason Naruto flees, like if Sasuke is being manipulated by an enemy and Naruto has to leave to save him. Or he could be chasing after Naruto, thinking Naruto has gone rogue.
Sure, there are fanfictions where Sakura isn't from Konoha. Fanfiction gives creators the freedom to reimagine the Naruto universe. Maybe in a particular fanfic, Sakura hails from a small, isolated ninja village that has been at odds with Konoha in the past. This origin would color her view of Konoha and its ninja, and would also change how she is perceived by the Konoha characters. It's all about exploring new creative directions within the Naruto fanfiction world.
There could be a power vacuum. Naruto and Sakura are two of the most powerful ninja in Konoha. Their absence may leave the village vulnerable to attacks from outside forces. Other villages might see this as an opportunity to gain an advantage over Konoha.
Maybe he feels betrayed. In the original story, Naruto has faced a lot of discrimination in Konoha when he was young. So in the fanfiction, it could be that some similar or new issues make him decide to hide.
One reason could be to seek greater power. Maybe they feel that Konoha no longer offers the training or resources they need to reach their full potential. So they decide to leave and explore other places where they can become stronger.
To change her character dynamics. In fanfiction, if she's not from Konoha, her relationships with characters like Naruto and Sasuke will be different. Maybe she has a different loyalty or a different set of goals that are not related to Konoha's well - being.
Well, in this Konoha High School fanfiction, Naruto's character could be more laid - back. He doesn't have the same heavy burden of being a jinchuriki. He's more interested in impressing Sakura with his school achievements rather than his ninja skills. Sakura might be less tough - minded when it comes to fighting. Instead, she's more concerned about her reputation in school. For example, she might worry more about getting good grades and being popular rather than being a great ninja.