They would probably have a very close and mentor - student relationship. Kakashi, being Naruto's caretaker and trainer, would be like a father figure to him. Naruto would look up to Kakashi and trust his guidance completely.
Well, Kakashi could train Naruto in combat skills specific to ANBU missions. This would include more lethal and precise attacks. He might also teach Naruto how to use different types of weapons that are common in ANBU operations. Maybe Kakashi would set up mock battles where Naruto has to face multiple opponents at once, just like in real ANBU scenarios.
They could develop a mentor - apprentice relationship. Kakashi already has some experience mentoring Naruto, and in the ANBU setting, he could teach Naruto more advanced and stealthy techniques. Naruto would look up to Kakashi even more and try to learn as much as he can.
Communication is key. If they sit down and talk about their misunderstandings and feelings, it could start to mend their relationship. Naruto could express his frustrations, and Kakashi could explain his actions.
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.
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.
Flashbacks can also play a crucial role. By showing their past interactions, even if brief, it can add depth to their relationship. Maybe a flashback of a time when Naruto was a child and Kakashi saved him secretly in his Anbu days. This would create an unspoken bond that could be explored further in the fanfiction.
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.
One common theme is loyalty. In the ANBU, loyalty to the village is of utmost importance. Fanfictions often explore how Naruto and Kakashi uphold or struggle with this loyalty. For example, they might face a situation where their loyalty to each other conflicts with their loyalty to the village.