Yes, there might be. The world of fanfiction is vast, and with the popularity of both Naruto and Kaido from different fictional universes, it's not unlikely that someone has created a crossover fanfiction where Naruto has some sort of connection to Kaido. You can search on popular fanfiction websites to find out.
There is a novel called " A Man Marries Kaido's Daughter at the Beginning of the Pirates " that might fit your needs. The plot of this novel was full of ups and downs, and it was exciting. It was a good book with good plot and writing. You can find the latest chapters on the website provided by Grimm Literature for free and read them online.
In 'luffy vs kaido fanfiction', Luffy's growth and new abilities are often explored. He might develop new forms of his Gear powers to face Kaido. Kaido, being extremely powerful, forces Luffy to push his limits. Fanfictions may also focus on the intense battle scenes, with detailed descriptions of their attacks and counter - attacks.