So I thought about what happens when you die in Naruto, and then this came to mind. It's not just Shaman King, it's also a little bit of Yuragi-sou no Yuuna-san. Mainly, I'm going to be drawing from Kogarashi's tendency of being possessed and gaining new skills. First, we're going to be talking about what kind of techniques are going to appear. Be fore-warned, I don't know jack about Shaman King beyond what I can find on Wiki's. I know Shaman can't be possessed without permission, but we'll just say that the MC doesn't learn that until he's a teen or adult.
All that really is going to be used is Over Soul, which is going to take some imagination. Specifically because of the possible dead shinobi to use. Aside from Minato Namikaze, until Orochimaru frees him from the seal, everybody else is fair game. Kushina, Hashirama, Mito, Tobirama, or any of the Uchiha killed during the massacre. Hell, you could even figure out a way to give the MC one of the Seven Swords of the Mist and have that be his medium for his Over Souls. Or you could bring over the Futsunomitama no Tsurugi (Not sure how it's supposed to be formatted) as their Clan treasured weapon. I imagine that Hashirama's Over Soul would involve his Mokuton, Tobirama's would be his Space-Time Jutsu or his mastery over Water. Kushina's would most likely involve the Adamantine Sealing Chains and Mito's would be something similar or just Seals in general. I can't actually tell if I'm using Over Soul right, but feel free to correct me in the comments.
Onto the Yuragi-sou part: I want the MC to be possessed several times while growing up so they can learn various Shinobi skills, such as Ninjutsu, Sealing, Kenjutsu, Taijutsu, as well as survival skills like cooking, trapping, hunting, and butchering. He would also have an immense pool of Chakra similar to Kogarashi's ridiculous amount of Spiritual Power due to being the Yatahagane. I also think you could figure out a way to bring in the Spiritual Armor from the series, and have it act as special gear for the Asakura head and heir.
This idea was written as an insert plot, but I can see it just as easily being used as a reincarnation plotline. As an example, a man dies and is given three wishes. He wishes to be reborn in Naruto, along with being born into the Asakura Clan, and having Kogarashi's immense spiritual energy pool/ Uzumaki level chakra.