The two heroes-in-training were paired together during the Battle Trial and the Unforeseen Simulation Joint, showing to working well together. They also studied together under Momo's tutelage.
Though the two can hold casual conversations, most of the time they will argue. Even more likely, Kyoka will teasingly tell Denki rude things that will get on his nerves, like happen to find his brainless state uncontrollably funny.
Despite this, in the recent chapters of the manga, Denki is shown to hold Kyoka at a greater respect due to her talent in music and even gives encouragement to the point of flustering her.
In Chapter 263, Denki is told by Midnight to think of those he cares about the most, and soon afterward, Kyoka is shown. Additionally, Denki remembers a moment where he was practicing for the School Festival, with Tokoyami, and in that moment, he shows how much he respects her, and this motivates him to keep fighting. Denki considers Kyoka is one of the most important person to him and the main reason he gained confidence in his battle in the front lines. Kyoka and Denki are reunited in chapter 278 with Denki asking a terrified Kyoka "What's wrong Jiro Jack?" after gigantomachia starts approaching them. During Class A and B's attempt to stop gigantomachia from proceeding any further, Kyoka ears are burned by Dabi's flames and Denki is heavily injured by debris mid air by Mr. Compress's marbles. Despite all their efforts, they were unable to stop gigantomachia as he went on a rampage. They were forced to flee and were luckily saved by Majestic's quirk in chapter 283.
As well as that, in the OVA Training Camp of the Dead, Denki is seen holding Kyoka up when she is in pain due to an attack from Katsuki. This is not technically a canon fact in terms of plot, but hints that the people behind the anime do support this ship.
In My Hero Academia: Smash!! during his internship, Kaminari called Jiro. When she hung up, Kaminari can be seen smiling saying "that takes me to my happy place."
On AO3 it is the second most written ship for both Jirou and Denki. It is also the twenty seventh most written in the My Hero Academia tag.
Although their ship has long been considered a fairly local het variant for Jiro among people who don't ship MomoJiro, KamiJiro quickly gained explosive popularity after the events of manga and anime adaptation. The great emphasis on Kaminari helping Jiro during the festival arc at the end of the third season of the anime and his recognition of Jiro as his most important person in the manga chapters that were released at that time made many people sincerely believe that the relationship between the two has great potential.
Due to the fact that, unlike Momo, before that, Jiro almost didn't receive any straight teasing in story and was even widely interpreted as closet lesbian in fanon, the sudden popularity of the ship among fandom also gave rise to many jokes that MomoJiro or TodoMomo ceased to interest anyone and were forgotten.
And while TodoMomo fans generally supported KamiJiro as ship mates, MomoJiro supporters were generally dissatisfied with the rise in popularity of this ship, as it made her previous reading as a lesbian more debatable. At the same time, due to its greater popularity than TodoMomo, this ship didn't receive the same negative attitude in ship wars.