The cloak could make Naruto more confident. If it has special powers, he would feel more capable and in control. For example, if it gives him the power of invisibility, he might start to take more risks in battles and become bolder in his strategies.
One idea could be to have a character from Naruto end up in the Cloak and Dagger universe. For example, Naruto himself could be transported there and his unique abilities like the Rasengan would be a shock to the characters in that world. He might team up with Cloak and Dagger to fight against a common enemy, perhaps a group that is trying to steal the powers of both universes.
One interesting Naruto chakra cloak fanfiction could be one where Naruto discovers a new form of the chakra cloak with unique powers. For example, it might give him the ability to fly. Another could be a fanfic where he shares his chakra cloak powers with his friends to defeat a super - strong enemy.
First, you need to do your research on both Naruto and Cloak and Dagger. Know the characters, their powers, and the settings well. For example, in Naruto, the different clans and their jutsus are important elements. In Cloak and Dagger, the light and dark powers and the social issues in their world matter. Then, come up with a unique plot. Don't just copy existing storylines. You could start with a situation like a dimensional rift that brings the two worlds together.
Sasuke is also quite popular in these fanfictions. His relationship with Naruto, whether it's a rivalry or a more collaborative one in the context of the Kyuubi cloak powers, makes for interesting stories. For example, Sasuke might be jealous of Naruto's newfound power and try to surpass it in his own way.
It could be a new character created specifically for the fanfiction. Maybe a wandering ninja who uses the black cloak to hide their identity and past traumas.
One interesting Naruto fanfiction related to the black cloak could be about a mysterious character who wears a black cloak and has a hidden agenda within the Naruto universe. Maybe they are secretly working against the Akatsuki or have a connection to an ancient jutsu that only they can unlock while wearing the cloak.
Well, perhaps the cloak has a hidden power that is only unlocked when Naruto faces his greatest fears. It could be a power that not only enhances his physical abilities but also his mental strength. For example, when he's in a tough fight and on the verge of giving up, the cloak activates this power and he suddenly has the strength to keep going. Also, the cloak could have a connection to the Sage of Six Paths, and through it, Naruto discovers new secrets about his heritage.
Another plot could involve Naruto sharing his Kyuubi cloak powers with his friends. He discovers a way to temporarily transfer some of the cloak's power to them, and they use it to fight a new and powerful enemy that was too strong for them before. This would also strengthen their bonds and teamwork.