One idea could be a story where Batman has to team up with Killer Frost to stop a common enemy that is freezing Gotham City. They start off distrusting each other but as they face challenges together, they learn to work as a team.
A fanfic could explore a scenario where Killer Frost is actually an undercover agent sent to infiltrate Batman's world. Batman suspects her but she manages to deceive him for a while until he finally uncovers the truth. However, by that time, she has developed some feelings for him and has a change of heart.
Perhaps a fanfic where Killer Frost loses her powers and Batman helps her get them back. In the process, they travel to a mysterious place that is related to the origin of her powers. Along the way, they have to face many obstacles and their relationship evolves from just allies to something more like friends.