There could be. There are a lot of creative fans out there who come up with all kinds of unique story concepts. However, I'm not sure exactly where you would find it. You could also check Naruto - related forums where fans might discuss and share such fanfics. It might take some time and effort to search for it though.
You can try Archive of Our Own (AO3). It has a large collection of fanfics from various fandoms, including Naruto. Just use the search function and type in 'Kakashi x Itachi tickle' and see what comes up.
😋According to the information you provided, I recommend the following novels to you: "The Reborn Naruto Practitioner","The Strongest Naruto Kakashi", and "I, Kiha's Life Mentor". The female protagonists of these novels were all reborn through time, and the male protagonists were the temporary teachers of Sasuke Uchiha, Kakashi, and Kiba. I hope you like this fairy's recommendation. Muah ~😗
, I recommend the following two novels to you. They are both derivative doujinshi novels.
1. "Under the Bamboo Forest of Naruto": In this novel, a male protagonist transmigrated to the Naruto World and had the first confrontation with Kakashi in the game of Hurochimaru and the Fate of a Thousand Birds. He forced Orochimaru to defect in advance and snatched Asma's Guardians. He also became the guardian of Destiny's Child and changed the trajectory of fate. The main character isn't Kakashi or Weasel, but the storyline is interesting and worth a try.
2. "Naruto's First Love": This novel is about Kakashi and Weasel's story. It is divided into volumes and the story is independent. Every "shadow" can have their own first love. Although the male lead was Kakashi, Weasel was also an important character. The plot was exciting and interesting.
I hope you like my recommendation, Mwah ~😗
Often, Gai is paired with Kakashi in Hurt Kakashi fanfiction. Gai, with his unwavering belief in friendship and his eternal rivalry with Kakashi, can be a great character to interact with a hurt Kakashi. He might try to pull Kakashi out of his slump through their friendly competition. Also, Rin is sometimes included. Since she has a significant past with Kakashi, her presence in the fanfiction can either be a source of comfort or more pain, depending on how the story is written.
Wonder Woman is another character that might be paired with Itachi. Her Amazonian warrior heritage and Itachi's shinobi skills can be compared and contrasted. Their different views on justice, with Wonder Woman coming from a more idealistic place and Itachi having a more pragmatic approach, can lead to some great character - driven storylines in fanfiction.
Naruto is often a common character. Since Naruto has a strong bond with Kakashi, he might be involved in Kakashi's time - traveling adventures. Sasuke could also be there. Their relationship with Kakashi in the original story makes it likely for them to show up. And of course, Guy would be a great addition. His friendly rivalry with Kakashi would add some humor and action to the time - travel scenarios.
Naruto would adapt to Itachi's life in several ways. Socially, he'd have to get used to Itachi's connections and rivalries. For instance, his relationship with Kisame would be different as Naruto. He might try to influence Kisame in a more positive way. Emotionally, he'd have to deal with Itachi's internal struggles. Itachi had a lot of guilt and secrets, and Naruto would have to either come to terms with them or find a way to resolve them. And in terms of combat, he'd practice Itachi's signature moves over and over to make sure he could use them effectively in battle.