One common theme is the power dynamic. Fat Gum has a lot of strength and experience, while Fem Kirishima might be portrayed as more of a newbie or someone looking to learn from him. Their relationship can develop around training and growing stronger together.
You can start by looking on fanfic websites like Archive of Our Own (AO3). It has a large collection of My Hero Academia fanfics. Just use the search function and type in 'MHA Fem Kirishima x Fat Gum' and you'll likely find a bunch of relevant stories.
One possible analysis could be that their relationship in fanfic often showcases a strong bond of friendship. Bakugo's explosive personality and Kirishima's more stable and friendly nature create an interesting dynamic. Fanfic writers may explore how they support each other during battles or in their daily lives at school. For example, Kirishima might be the one to calm Bakugo down when he gets too riled up, and Bakugo could inspire Kirishima to be more confident in his abilities.
Kirishima is still alive in the manga. The story doesn't have that plot point. Usually, character deaths are significant events and are clearly shown if they occur.
Another characteristic is the exploration of his relationships. His friendship with Bakugo is a popular theme. Fanfics might show how they support and challenge each other. Also, his relationships with his other classmates are often explored, like how he can be a source of motivation for them.
Kirishima is from a manga/anime. His back story involves him having a sense of self - doubt initially. He admired those with strong and manly qualities. He worked hard to overcome his insecurities and develop his own strength and courage, eventually becoming a reliable hero - in - training.
The theme of hidden pain is also prevalent. Kirishima, being a character who is often seen as strong and upbeat, in these fanfictions has a side of him that is filled with pain and sadness that he tries to hide from others, which is a very interesting and complex exploration of his character.