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.
In a straight - up fight, Itachi has some very powerful abilities. His genjutsu can be extremely difficult to break out of, and his ninjutsu attacks are strong. But Batman is no slouch. He has fought against some of the most powerful villains in the DC universe. He would study Itachi's moves and try to find a pattern. Batman might also use his wealth to create some sort of countermeasure to Itachi's Sharingan. Overall, it's a very close call and would likely depend on how the writer of the fanfiction wants the story to go.
One could be a story where two Tamil actresses, say Nayanthara and Keerthy Suresh, are in a fantasy world. They find themselves in a magical forest where they have to fight off dark magical creatures to protect a precious gem. Nayanthara uses her quick reflexes and a magical sword she discovers, while Keerthy Suresh uses her intelligence to outwit the creatures and they combine their powers to defeat the final big bad monster.
Minato might also be a prominent character. As their teacher, he can influence the way Obito and Kakashi interact. In some fan fictions, he could be the one to help them resolve their differences or provide some crucial information about their past that changes their current situation.
The theme of redemption also pops up often. Since Itachi has a complex and somewhat dark past, the OC might be a factor in his journey towards redemption. And for Kakashi, the OC could be a new chapter in his life, helping him move on from past traumas or regrets. This makes for a very interesting dynamic in these fanfictions.
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.
One interesting scenario could be a battle in a dark, abandoned cityscape. Itachi's Sharingan abilities would give him an edge in terms of perception and illusions. Batman, on the other hand, would rely on his gadgets and combat skills. He might use smoke bombs to disrupt Itachi's line of sight and then try to get in close with his martial arts. Another scenario could be a mental battle. Itachi is used to psychological warfare, but Batman is also a master of getting into his opponents' heads. Itachi might try to use his genjutsu to break Batman's will, but Batman's strong mental discipline could resist it.
One interesting scenario could be a battle of wits. Itachi is known for his intelligence and Sakura has grown to be a very smart and capable ninja. They might engage in a mental duel where they try to outmaneuver each other with strategic moves and mind games.
Some fanfictions might explore the emotional aspect of their fight. For example, how their past friendship affects the battle. Maybe Kakashi hesitates to strike a fatal blow because of their shared history.
In RWBY fanfiction, the Weiss vs Winter fight can be a display of their different combat styles. Weiss is more about grace and precision with her Glyphs, while Winter, being more experienced, has a more refined and perhaps harsher style. Their fight could also explore their complex relationship as sisters.