I am not familiar with the contents of any of the movies. Keeping this in mind, can anyone tell me if Naruto ever gets the promotion to chūnin (or Jōnin for that matter). Since he is clearly the Hokage in the last chapter of the manga, I wonder if he was made such while officially still a genin.
No, it was never shown in anime or OVA or manga (at the time of this answer)
Naruto didn't become chūnin in first chūnin exam, he missed the second chūnin exam due to his training with Jiraiya.
There is third chūnin exam mentioned in an OVA:
Chūnin Exam on Fire! Naruto vs. Konohamaru!
Where Naruto only got one hit but lost due to getting disqualified for using sage mode. But the same OVA also shows him qualified too:-
In the end, Kakashi, Gaara and the others comfort Naruto by letting him know he can become a chūnin anytime he wants, as he has already surpassed his contemporaries, including Kakashi himself.
why would he disqualified for using Sage Mode ? Jun 3, 2016 at 3:10
@NamikazeSheena Some jutsu seems forbidden in chunin exam. Jun 3, 2016 at 5:34
that's stupid. Do you think in a mission enemy shinobi will hold back when attacking? Jun 3, 2016 at 5:43
@NamikazeSheena If i am not wrong then there were limitations in chunin exams from start Jun 3, 2016 at 6:19
@TanyavonDegurechaff that's because the other participants are ordinary ninjas. They are not on Naruto's level. It would be ridiculous for them to fight someone that can defeat Pain of Akatsuki in full force. The limitation was to give them a fair chance.– 絢瀬絵里Dec 20, 2017 at 15:05
No Naruto never becomes chunin in the series nor is he ever chunin. After the war and Kakashi becomes hokage, Naruto studies to become straight to jonin (anime) bypassing the chunin stage. It obviously makes sense that Naruto never becomes chunin as he is well over jonin level by the end.