Perhaps in 'barry meets the justice league fanfiction', Barry first has a bit of a misunderstanding with the Justice League. He might be mistaken for a threat because of his speed being so extraordinary that it startles the other members at first. But then, after some communication and realizing they are all on the same side, they start to collaborate. Barry could teach some of the members how to better react to fast - moving threats, and in return, he could learn new combat techniques from them.
Well, it could be that Barry meets the Justice League during a crisis. He could use his speed to quickly gather information and then work together with the League to come up with a strategy to save the day. For example, he could run around the world to find out where the source of a powerful threat is located and report back to the Justice League in no time. And then, each member of the League, like Superman using his strength, Batman using his intelligence, and Wonder Woman using her combat skills, along with Barry's speed, they could combine their powers to defeat the enemy.
In this fanfiction, Barry might have some amazing speed - related adventures with the Justice League. Maybe he shows off his super - speed to the other members in a training session and impresses them all.