What does Barry mean when he tells Oliver he wants to kill fanfic?
Barry could be feeling protective of their story and image. Fanfic can sometimes go in wild and unexpected directions that might not align with how he or Oliver see themselves or their relationship. He may want to 'kill' fanfic to stop any false or inappropriate ideas from spreading. Also, he might be concerned that fanfic could influence public perception of them in a way that he doesn't want. For example, if a fanfic portrays them in a negative or untrue light, it could affect how their fans and the general public view them.
It's hard to say exactly without more context. Maybe he has a strong dislike for fanfic related to their world or characters. It could be that he feels fanfic distorts the 'true' story or characters in some way that he doesn't like.
Well, perhaps Barry has had some negative experiences with fanfic. Fanfic often involves a lot of creative interpretations of characters and storylines. It's possible that Barry believes these interpretations are ruining the essence of the original story he and Oliver are part of. He might think that by 'killing' the fanfic, he can preserve the integrity of their real - life (in - the - show) adventures and relationships.