I was thinking about Chidori and now I'm interested in it. I stumbled upon this question: can a ninja learn how to use Chidori and use it without Sharingan?
Yes it is, but there is a cost, Tunnel-vision. Kakashi invented the attack and used it without the Sharingan, and were it not for Minato, he would have been killed by one of his opponents. He is running so fast, and is focused so much on his attack, that he is unable to really focus on anything except that right in front of him when attacking. The second Paragraph of the overview on the wiki confirms this
The speed at which the Chidori is performed, despite being one of its greatest assets, also represents one of its biggest drawbacks: users move at their target so fast that its causes a tunnel vision-like effect for them. Because they charge in a straight line it is easy for opponents to attack them, and because of the tunnel vision it is difficult for the user to see these attacks, much less react to them. For this reason, most ninja cannot use the Chidori safely. If the user has a Sharingan, however, these drawbacks are overcome: the Sharingan's heightened visual perception prevents the tunnel vision from occurring and its predictive capabilities make it easy for the user to avoid counterattacks.
Kakashi's page summarizes the event itself
Kakashi tried to eliminate him with his new jutsu, Chidori, but the attack speed left him vulnerable to counter-attack, forcing Minato to step in, save Kakashi, and kill Mahiru himself. Before leaving them, Minato advised Kakashi to not use the Chidori again. ... After Rin transplanted Obito's Sharingan into him, Kakashi confronted Kakkō. His White Light Chakra Sabre was destroyed during the ensuing fight, but he succeeded in killing Kakkō with Chidori; due to the Sharingan's heightened vision, Kakashi was finally able to handle its speed.
If you think about it logically, many enhanced sensory abilities would counteract tunnel vision and allow you to use Chidori effectively. Byakugan totally eliminates any notion of tunnel vision. That's one of its main purposes. Sensor techniques, including Sage mode sensing, Mind's Eye of the Kaguya, and Mu's technique would provide the same advantage. While Karin was unable to take full advantage of her technique, due to her incompetent taijutsu, someone like Kakashi in possession of the technique would be quite capable of using it in combat to eliminate any possibility of tunnel vision. Mu actively demonstrated his ability to avoid attacks from his blind spot. Naruto's and Kabuto's threat perception both demonstrated this ability against high speed attacks. If they possessed Chidori, they would have no trouble utilizing it. If Ranmaru's Kekkei Genkai were cannon and in the possession of someone like Kakashi, tunnel vision would instantly cease to be an issue.