In a 'Naruto father of Kakashi' fanfiction, it might start with some kind of magical or mysterious event that makes Naruto become Kakashi's father. Naruto, with his strong will and positive attitude, could teach Kakashi different values. He might introduce Kakashi to his friends like Sasuke and Sakura in a new context. Also, Naruto's experience with the Nine - Tails could play a role in how he protects and guides Kakashi. And it could change the whole story of Kakashi's life, including his relationship with Obito and Rin.
Well, a 'Naruto father of Kakashi' fanfiction would be a wild departure from the original Naruto lore. Since Naruto is from a later generation, for him to be Kakashi's father, the story would have to rewrite a lot of the backstory. Naruto, being the father, would likely pass on his ninja way to Kakashi. He might have a different approach to training Kakashi compared to the traditional ways in the Hidden Leaf. Maybe he'd focus more on emotional strength rather than just physical and jutsu training. It could also lead to some interesting interactions with the other characters in Kakashi's life, like his teammates Obito and Rin, as Naruto's influence could change the dynamics of their relationships completely.
It would be really strange. Naruto is much younger than Kakashi in the original story. But if it were a fanfiction, maybe it could involve some time - travel or alternate universe concept. Naruto could use his experiences to raise Kakashi in a different way than Sakumo did.