Maybe it's a completely new and unknown kami. A kami created specifically for this fanfiction. This kami could have unique powers and a different view of the ninja world compared to the existing characters in Naruto. It would add a fresh and exciting element to the story.
Maybe it's an existing character from Naruto who has been elevated to Kami status. For example, Tsunade could be turned into a Kami, and Naruto's relationship with her could be a very different dynamic from their previous ninja - leader relationship. Or it could be Kaguya, who was already a very powerful being, and in this fanfiction, she reforms and becomes a Kami and Naruto's wife.
In fanfiction, the 'kami' could be an original deity created by the author. This new 'kami' could have its own motives and reasons for giving a gift to Naruto. Maybe it's a kami that has been observing Naruto's journey and decides to interfere to help him achieve a greater purpose. It could be a kami associated with nature, like a kami of the wind or the fire, and the gift could be related to that element.
In a 'naruto adopted by kami fanfiction', perhaps the kami takes Naruto to a different dimension where he trains in secret. There, he learns unique jutsu and fighting styles. When he returns to the Naruto world, he surprises everyone with his newfound abilities and a more confident attitude. He might also use his connection with the kami to bring peace to the ninja world.
Perhaps it could be a female version of an existing kami from Naruto lore. For instance, a female counterpart of the Sage of Six Paths. She would have vast knowledge and power, and her training of Naruto would be a way to pass on that ancient wisdom and strength.
Maybe Jiraiya. Since Jiraiya was Naruto's mentor and taught him a lot of things. He might have some knowledge about summoning kami and pass it on to Naruto.
In such a fanfiction, Naruto might gain divine powers. Since Kami is a powerful entity, Naruto could be trained in ways that are far beyond what he learned in the ninja academy. He might also have a different perception of the world and his place in it, seeing things from a more god - like perspective.
Ino could be a potential member. Since she has a strong connection with mind - related abilities, she might be intrigued by Naruto's new connection with fem Kami and get involved in the harem. Also, Sakura might be part of it. Despite her initial feelings for Sasuke, she could see Naruto in a new light after his encounters with fem Kami and join the group.
It could be about Naruto obtaining kami - like powers. Maybe he discovers he has a connection to the kami and has to learn how to control these new powers to save the Hidden Leaf Village from a great threat. Or perhaps he is chosen by the kami to be a sort of bridge between the human and divine worlds in the Naruto universe.
Sasuke could also be a great main character for this kind of fanfiction. With his already complex character arc in the original series, adding the kami bloodline to his story could take it in new and exciting directions. He could struggle with the power of the bloodline, perhaps fearing it would make him too much like those he has fought against in the past, or he could use it to seek revenge in a more powerful way than before.
Obviously, Kami would be the main antagonist. Since the title says 'naruto betrayed by kami', Kami is the one doing the betraying, which makes him the bad guy in this fanfiction.