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.
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.
In fanfiction, Naruto creating Chidori could be possible through some creative plot devices. Maybe he was taught by Sasuke in an alternate universe where they teamed up earlier. Or perhaps he discovered a scroll that had the knowledge of Chidori and was able to learn it on his own with his determination and quick - learning ability.
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 fanfic where Naruto knows the Chidori, it could change the power dynamics in battles significantly. Naruto's already vast chakra reserves combined with the piercing and fast - acting nature of the Chidori would make him an even more formidable opponent. He could use it in close - quarter combat situations, perhaps integrating it with his Shadow Clone Jutsu in creative ways. For example, he could have clones perform the Chidori from different angles, catching his enemies off - guard.
He might combine the Chidori with his Sage Mode. In Sage Mode, Naruto has enhanced senses and strength. Adding the Chidori to that would make it an extremely powerful attack. He could use the precise and fast - paced nature of the Chidori while being in Sage Mode, which would give him better accuracy and more power behind the jutsu.
It would make him more versatile. He's known for his Rasengan, but using the Chidori would show that he can adapt other powerful techniques. This could make him seem more of a prodigy, as the Chidori is a difficult technique.
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 the fanfic, Naruto could use the Chidori to save his friends who are trapped by an enemy's powerful jutsu. Since the Chidori is a very fast - moving and piercing attack, he could break through the barriers set up by the enemy. He might also face some internal struggle as using the Chidori goes against his normal style of ninjutsu.
There could be many 'sakura learns chidori fanfiction' out there. Maybe you can ask in relevant anime or Naruto fan communities. They might be able to point you to some good ones. Sometimes, these fan communities have their own collections or recommendations for such fan - made stories.