The dwarf in The Hobbit who is Kíli’s brother is Fíli.
Fíli and Kíli are the two youngest members of Thorin Oakenshield’s company. They are sons of Dís, Thorin’s sister, making them Thorin’s nephews and descendants of the royal line of Durin. Their youth is emphasized when Tolkien describes them as noticeably younger than the other dwarves.
The pair are often remembered together because they travel as a close-knit team throughout the quest from Bag End to the Lonely Mountain. In the book, Fíli is the older brother, while Kíli is five years younger. The Peter Jackson films expand their individual roles, especially Kíli’s storyline with Tauriel, a character created for the films rather than Tolkien’s novel.
A darker neighbouring fact is that both brothers die during the Battle of the Five Armies. They fall while defending their uncle Thorin, who is mortally wounded in the same battle. Fíli is therefore not merely another member of the company: he is Kíli’s older brother and a potential heir to Thorin’s kingdom.