At first, it might be a bit rocky. Kakashi is used to his own ways, and fem Naruto may be a bit headstrong. But as time goes on, they start to understand each other. Kakashi sees her potential and determination, and fem Naruto starts to respect Kakashi's wisdom.
In such a fanfiction, their relationship could develop in various ways. Naruto might start leaving little gifts for Kakashi anonymously. This would pique Kakashi's curiosity. Eventually, when he discovers it's her, he could be touched. Then they might start spending more time together during training or on missions, and their bond would grow deeper from there.
It would be very close. Kakashi would be like a father or an older brother to them. Naruto and Sasuke would respect and rely on him. They would probably have a more harmonious relationship with each other too, because Kakashi would be there to mediate any conflicts.
Their relationship would likely become very close. Naruto would probably start to see Kakashi as a father figure. Kakashi, in turn, would become more protective of Naruto.
The appeal lies in the potential for new character dynamics. Since Naruto is female in this concept, her interactions with Kakashi can have a different emotional undertone. It could be a more nurturing relationship, with Kakashi seeing her as a protege in a different light.
At first, Naruto might be a bit scared or hesitant. But as the fem Kyuubi shows her caring side, like protecting him from danger, Naruto starts to trust her. As time goes on, they become more like family. The fem Kyuubi shares her wisdom with Naruto, and Naruto in turn shows her the value of human emotions.
Well, it could strain their relationship. Avoidance usually creates distance, and in this case, Kakashi might feel hurt or confused as to why Naruto is avoiding him.
Their relationship is like a mentor - mentee bond. Kakashi has trained Naruto, and when he sees Naruto achieve great things, it can be overwhelming. For example, when Naruto masters a new jutsu that Kakashi thought was difficult for him, Kakashi might cry out of joy for Naruto's accomplishment.
It could become strained. Naruto snapping at Kakashi would create an initial rift between them. Kakashi might be taken aback by Naruto's outburst and Naruto, after snapping, might feel a bit guilty but also stubborn about his feelings, which would make the relationship tense for a while.
Kakashi may become more fatherly. He starts to show more emotions and care, different from his usually aloof self in the original series.
In many fanfictions, Fem Naruto might show kindness towards the Kyuubi. This kindness could be something the Kyuubi has never experienced before. For example, instead of just seeing it as a source of power, Fem Naruto might try to understand the Kyuubi's past and pain. This could lead to the Kyuubi gradually opening up to her and them developing a deeper bond.