Maybe Sasuke teaches him the Chidori in a moment of camaraderie. And for the Rasengan, it could be an older and wiser Naruto from the future who travels back in time to teach his younger self.
It could be Kakashi. Since he's already Naruto's teacher and he knows both techniques. He could guide Naruto in understanding the intricacies of the Chidori, like how to form the lightning - chakra in his hand, and for the Rasengan, he could give more advanced tips on chakra control.
In a fanfiction like this, the plot might involve Naruto struggling to master both techniques. He could start by observing Sasuke use the Chidori and then try to incorporate its lightning - based power into his own jutsu. For the Rasengan, he might have new insights while training, perhaps finding a way to combine it with the Chidori for an even more powerful attack. Along the way, he would face challenges like controlling the chakra flow for both techniques and dealing with opponents who are also after these powerful jutsus.
Well, he might start with intense training sessions. Maybe he observes Kakashi closely for the Chidori, and for the Rasengan, he practices over and over again, gradually getting the hang of the chakra control required.
In many Naruto fanfictions, the Chidori - Rasengan combo is often portrayed as an extremely powerful and unique move. It combines the piercing nature of the Chidori with the rotational and explosive force of the Rasengan. Some fanfictions might have Naruto or Sasuke (or both in some cases) creating this combo during a crucial battle against a powerful enemy, like a new Akatsuki member or a rogue ninja from another village. This combo is usually described in great detail, with the lightning - chakra of the Chidori surrounding and enhancing the Rasengan, making it not only more destructive but also having an added effect like paralysis due to the electricity.
In a more creative fanfic, an ancient ninja who was the originator of the Chidori technique could appear. This ninja could be brought back to life through some sort of magic or jutsu. He sees Naruto's pure heart and decides to pass on the Chidori knowledge to him, believing Naruto will use it for good.
In many fanfictions, Naruto might master the Rasengan through intense and unique training methods. Maybe he gets some special guidance from an unexpected source, like a hidden shinobi in the village who has a different perspective on chakra control. This person could show Naruto some new ways to focus his chakra, which finally enables him to form the Rasengan successfully.
In some fanfictions, Kakashi could also play a role. He is very knowledgeable and has seen the Rasengan in action. He might offer some tips on chakra control, which is crucial for Naruto to master the Rasengan.
Sasuke could be Naruto's teacher. Since Sasuke is a master of the Chidori, he might decide to teach Naruto as a way to make Naruto a more formidable ally. They have a complex relationship, and this could be a way to strengthen their bond.
One possible scenario could be that Naruto learns the Chidori from Sasuke in a moment of truce. Sasuke, realizing Naruto's determination to become stronger, decides to teach him this powerful jutsu. Another could be that Naruto discovers a scroll that contains the secrets of the Chidori and through his own hard work and study, he manages to master it. Or perhaps, a new character appears who has knowledge of the Chidori and trains Naruto in it as part of a greater plan to defeat a common enemy.