To gain knowledge. Stories can be a great source of knowledge, and Killmonger might read them to learn about different cultures, strategies, and ways of thinking. This knowledge can then be used in his quest for power and revenge.
Maybe he reads stories about power and revenge. Since Killmonger is a complex character who is obsessed with power and getting revenge on those he believes have wronged him and his people, stories with such themes might appeal to him.
There are fanfictions that might focus on an alternate universe where Killmonger survived. In this scenario, he could be on a path of redemption. He might use his intelligence and skills to actually help Wakanda in a more positive way, instead of trying to take over by force.
One great aspect of Black Panther and Killmonger fanfiction is the exploration of different character arcs. For example, some fanfictions might focus on a scenario where Killmonger had a change of heart earlier in the story. This could lead to him and Black Panther working together to improve Wakanda in ways that were not possible in the original movie. It gives a chance to see different sides of their personalities and how they could grow and develop in new situations.