KyoRi

"Kyo: The flames are calling you! Iori: Then let it burn, as it demands."

- The King of Fighters '98, Iori vs Kyo battle intro.

KyoRi mostly known as Iori x Kyo or Kyo x Iori in the west, as well as 庵京 and 京庵 respectively in the East, is the pairing between Kyo Kusanagi and Iori Yagami from the King of Fighters fandom.

Canon
Kyo Kusanagi 草薙京 is the titular protagonist in The King of Fighters video game series. Iori Yagami 八神庵is Kyo's rival who first appeared in the second title of the series KOF95.

Kyo is the heir of the Kusanagi Clan, one of the three clans that sealed the legendary snake entity, Orochi, 1800 years ago. His family's treasure is the Kusanagi Sword (草薙（の剣, and his family crest is the sun.

Iori is the heir of the Yagami clan (Former Yazakani clan) His family's treasure is the Yasakani Jewel 八尺瓊曲玉 and his family crest is the crescent moon.

Kyo's official nickname is "Scion of the Flame" 炎の貴公子 or "The Cleansing Exorcising Flame" 火炎 祓濯

Iori's official nickname is "Flame of the End" (終焉の炎. In XII, XIII and XV, it later translated to Unshackled Instinct 解き放たれし本能 in XV.

Personalities
Kyo is the over-confident but well-meaning protagonist of the series, more interested in enjoying life than having to partake in any particular responsibilities. He is quick to dismiss subjects that don't interest him and will often carry out his actions with a devil-may-care attitude. Despite his seemingly arrogant and rude demeanor, he treasures his friends and family.

Iori is a serious, blunt and rude character. He is not interested in making friends or enemies, only showing investment in getting results that appeal to him. He may seem to be incapable of acts of kindness or empathy but he isn't antagonistic nor mean outside of combat.

Official relationship
Kyo takes his clan's responsibilities on a more personal level, disregarding ancient legends and predestined events as any reason for his actions. His rivalry with Iori Yagami is not spurred by their clans' history, and partly due to Iori's prior aggression. While he will fight Iori, he won't go as far as to kill him, being aware of his role as a part of the Three Sacred Treasures. When Kyo and Iori join forces, it is often begrudgingly and as a last resort solution to the conflict at hand, with seemingly no desire to seek lasting and mutual peace, particularly on Kyo's part. However, he will leave Yagami alone as long as Iori doesn't seek to antagonize him as usual, and will respect his actions, especially if it involves their clan responsibilities.

Recent portrayals of Iori and Kyo, his willingness to set his murderous vendetta aside on multiple occasions and the semi-canonical SNK Heroines strongly suggests he's no longer as homicidal as he once was, particularly with Kyo, clashing with him only for the sake of show of strength and to keep Kyo on his toes.

Official Music
Kyo and Iori have 2 official duet songs that made fans wonder about their feelings for each other.

Yuuhi to Tsuki (と, Yuuhi to Tsuki, lit. The Setting Sun and Moon) KOF96

https://youtu.be/TewxqaL1bcA

King of Fire (From KOF for Girls Battle Song Album )

https://youtu.be/PHGwESpphCo

Fanon
There are multiple interpretations of their relationship depending on the author. Since this pairing started in the 90s the perception of the characters had evolved with the years and the current content of the ship is very different from the way it started.

In the first games (Orochi saga) Iori chased Kyo obsessively. Doujin and fanfics from those times reflected his obsession with killing Kyo and often showed Iori being dominant and aggressive and Kyo being aloof and carefree.

During the early 2000s, in the NESTS saga, a lot of the Doujin and fanfics had a dark and melancholic vibe following the canon lore of the games. Some stories included K' as another love interest for Kyo or Iori.

During the Ash saga, it was common to find Doujin and fanfiction in which Kyo took action and chased Iori, changing their dynamic. This is mostly due to an official novel from KOF12 in which Kyo looks for Iori and he is quick to point out that this time Kyo is the one who is looking for him and not the other way around.

SNK Heroines and the existence of Miss X also inspired fans to create Doujin, fanart, and fanfiction of Kyo x Miss X. The female versions of both Kyo and Iori are also popular, especially among Asian authors who to this day create content of them (in this case it becomes Girls Love)

Fandom
FAN FICTION

Media
https://www.youtube.com/watch?v=s7TdMdYw5Fk

https://www.youtube.com/watch?v=XttKPhA1Czc

https://www.youtube.com/watch?v=YEaWqSpSVF0

https://www.youtube.com/watch?v=S_GXs7exNvQ

https://www.youtube.com/watch?v=Td9Mk65PDLg

https://www.youtube.com/watch?v=hVLmq-dGKEA