Some teachers might initially be scared and give in to the student's demands. For example, they might change grades or give special treatment as the student asks.
Some teachers react positively. They might see it as a sign of students' passion for reading and writing. They could use it to inspire students to explore more about Greek mythology which is a big part of the Percy Jackson series.
Toge Inumaki is important too. His special cursed speech ability makes him stand out. Also, the principal of the school, Masamichi Yaga, is likely to be important as he is in a position of authority and has an influence on Gojo and the other students. There could be other characters like the members of different clans that also play roles in the complex web of the story.
Flitwick might be quite intrigued. He loves magic in all its forms and fanfiction would show him new and different ways magic could be used in the Harry Potter world. He'd be interested in the creative spells and concepts that the fans come up with.