Yes, there might be some out there. You can try searching on specialized fanfiction websites. However, the availability can vary depending on the site's content policies and the popularity of such a specific genre combination within the Naruto fanfiction community.
One common theme could be the struggle of Naruto to master a new skill while also dealing with his relationships in the yaoi context. Another might be the power dynamics that come with learning kenjutsu and how it affects his interactions with other characters in a romantic or sexual way.
One possibility could be Kakashi. Since Kakashi is already a very versatile ninja with skills in many areas including some swordsmanship, he could teach Naruto kenjutsu. He has the patience and the knowledge to pass on the skills.
In a 'naruto learns kenjutsu fanfiction', one possible plot could be that Naruto decides to learn kenjutsu to diversify his combat skills. He might seek out a master swordsman in a hidden village. The master could initially be reluctant to teach him, seeing Naruto as a rowdy ninja. But as Naruto shows his determination and unique ninja way, the master changes his mind. Naruto then has to go through rigorous training, learning different sword stances and techniques. Along the way, he might face opponents who are skilled in kenjutsu and use those battles to improve his skills further.
In many fanfictions, Naruto might start learning kenjutsu as an adult to diversify his combat skills. He could learn from various characters, like Kakashi or even some new, original characters created by the fanfiction writer. This would add a new dimension to his fighting style, making him more versatile in battles against stronger opponents.
Maybe Naruto's learning of Uzumaki Kenjutsu is a result of some hidden Uzumaki clan heritage coming to light. He could be guided by an old Uzumaki clan member or some ancient scrolls. As he progresses, he faces challenges from enemies who fear his newfound power. And he has to use his kenjutsu skills to protect his friends and the village.
Naruto becomes more disciplined. Kenjutsu requires precision and control, which are different from his usual brash ninjutsu - based attacks. He has to be more patient and calculated in his moves.
Well, he might start by observing other kenjutsu masters. Maybe he watches Kakashi or other skilled swordsmen in the village. Then he'd practice a lot, like in his training with Rasengan but with a sword instead. He could also learn from old scrolls about different sword techniques.
One possible fanfiction could involve Naruto learning kenjutsu skills and Hinata being inspired by his newfound abilities. Maybe Naruto discovers an ancient sword technique and Hinata supports him in his training, leading to a deeper bond between them.
His opponents could include some of the samurai from the Land of Iron. They are known for their kenjutsu skills. Since Naruto is now a kenjutsu master in the fanfiction, there could be some sort of misunderstanding or rivalry that leads to battles between them. And, of course, there could be new villains created specifically for the fanfiction who are also masters of kenjutsu and pose a great threat to Naruto.