There are a countless number of reasons to ship them and their relationship has so much going for them. Since I'm not very eloquent in terms of speech, I'm going to cite a blog post from red-riot-kirishima-eijirou's Tumblr account.

1. Kirishima is important to Bakugou’s character development. 

Early on, he encourages Bakugou to have friends and allies by being a friend and ally to Bakugou himself. Kirishima does such a good job making himself a friend and equal to Bakugou that he becomes the only classmate Bakugou can accept being rescued by without hurting Bakugou’s pride. This is a huge step for Bakugou’s character development because it shows Bakugou can learn how to accept help from someone without his ego being bruised. 

2. Bakugou CARES about Kirishima. 

Usually Bakugou doesn’t give a crap if someone is sad. However, Bakugou has been shown multiple times trying to cheer Kirishima up when Kirishima is sad, which is something he hasn’t done for other classmates. Bakugou cares about someone besides himself, and the classmate Bakugou cares about the most is Kirishima. Bakugou doesn’t care about people like a hero should. As Bakugou learns to care about Kirishima, he can become capable of caring about other people, further showing how Kirishima helps Bakugou become a better hero.

3. Despite Kirishima admiring Bakugou and wanting to be his friend, Kirishima doesn’t let Bakugou walk all over him. 

He’ll tease Bakugou like any friend would, even if Bakugou doesn’t like it. And he doesn’t let Bakugou get away with shit. He understands Bakugou needs to improve his behavior and will call Bakugou out on his bad behavior. Kirishima won’t let Bakugou get away with not calling him by his name either. Kirishima not only wants Bakugou to be his friend, he also wants Bakugou to treat him with respect. Kirishima doesn’t want to be Bakugou’s minion. He wants to be his equal. 

4. This point goes without saying, but similar to how Bakugou cares about Kirishima, Kirishima REALLY cares about Bakugou. 

Kirishima is one of the people who is most worried for Bakugou when Class 1-A hears the villains are after Bakugou. And despite the dangers for him and his classmates, Kirishima is willing to break the rules to rescue Bakugou because he is one of the students hurt most by Bakugou’s capture. Kirishima checks to see if Bakugou passed the hero license exam and is worried about Bakugou when he sees Bakugou doesn’t pass. 

5. Bakugou respects Kirishima. 

Bakugou sees Kirishima as a useful ally because their Quirks work well together and is willing to accept Kirishima into his cavalry battle team as a result. Then during that cavalry battle, he listens to Kirishima when Kirishima tells Bakugou to calm down, and Bakugou even refers to Kirishima by his name, something Bakugou rarely does and only does with people he respects. Kirishima puts up a good fight against Bakugou during the Sports Festival, showing Bakugou that he’s more than just his hardening Quirk, making Bakugou respect him even more. Not only does Bakugou respect Kirishima enough to be rescued by him without hurting his pride, but Bakugou remembers words Kirishima told him months later. Kirishima told Bakugou he’d be unshakable during the cavalry battle, and then Bakugou recalls those exact words months later. Bakugou doesn’t remember things unless they’re important. The things Kirishima says have a huge impact on Bakugou. Furthermore, Bakugou thinks Kirishima is so strong that he states Kirishima can be unbreakable like All Might. Considering how highly Bakugou thinks of All Might, that’s a huge compliment and shows how much Bakugou respects Kirishima’s abilities. 

6. Bakugou is good for Kirishima’s character growth. 

Kirishima looks up to Bakugou for his unwavering determination and strength and tries to be a strong hero more like Bakugou. When Kirishima expresses how little he thinks of his Quirk and abilities, Bakugou gives Kirishima advice and helps Kirishima create his new super move, Red Riot Unbreakable. As demonstrated by Red Riot Unbreakable, Bakugou helps give Kirishima conviction and a more unbreakable spirit, making Kirishima more of an unyielding wall, which will improve Kirishima’s hero career. Kirishima wouldn’t be the mighty brute force he is now without Bakugou. In addition, the things Bakugou says improve Kirishima’s confidence. For instance, Red Riot Unbreakable raised Kirishima’s confidence and makes him feel stronger, which is important for Kirishima’s self-esteem. Keep in mind, Bakugou usually says things to hurt and lower other people’s confidence, so it’s very remarkable that the things he says helps Kirishima’s confidence instead. Although, it’s difficult for Bakugou’s threats and insults to faze Kirishima anyway. Considering Kirishima’s low self-esteem, Bakugou is an important person who’ll help raise Kirishima’s confidence. In addition, both Bakugou and Kirishima suffer from painful inferiority complexes, with Bakugou’s inferiority complex manifesting into a superiority complex. They can both relate to their issues and help each other. Overall, Bakugou and Kirishima’s relationship gets lots of development throughout the series. They mean a lot to each other and help their characters grow. They’re arguably best friends. They’re so close that Iida automatically turns to Kirishima when asking about Bakugou’s whereabouts. 

Not only do they have a lot of chemistry and compatible traits, as listed in red-riot-kirishima-eijirou's post, but it would be a progressive step in the shonen manga industry, that would provide inspiration for younger fans of the genre, who are of the LGBTQ community that would like to see a healthy same-sex ship portrayed in media. Not to mention it would provide fan service for many female/male fans whom are already passionate about the ship and see it's potential.

In conclusion, I believe Bakugou x Kirishima should be made canon in the series.

Source:  https://red-riot-kirishima-eijirou.tumblr.com/post/162846161017/i-love-kirishima-a-lot-and-i-love-your-blog