First, know the characters well. Read the comics or watch the movies to understand their personalities and backstories. Then, come up with an interesting concept like a new threat to Gotham or a change in the family dynamic.
To start writing batman bat family fanfiction, you need to pick a particular aspect of the Bat family you want to focus on. It could be the relationship between Alfred and the Bat - kids. Once you've chosen that, think of a plot that would be engaging. For example, Alfred having to keep the Bat - cave running while all the heroes are away. Also, don't be afraid to add your own twists to the established lore. Just make sure it stays true to the essence of the characters.