Info from the Wiki.

Thanks to his unique upbringing and family, Kohaku stands out as a rather old-fashioned individual. He speaks with a Kyoto dialect, often making obscure, old school-esque references. He is also surprisingly mature for his age, well-mannered, and eloquent.

Despite his cute looks and polite demeanor, however, Kohaku has a very sharp tongue. A no-nonsense type of person, he never sugarcoats his words, and isn't above threatening others (usually being genuine) if he's teased too much or finds himself irritated by the person in question. He also has a cynical worldview, often remarking on the evil in the world and his rather unfavorable self-image.

Although he doesn't show it easily, Kohaku does care deeply about his friends, and he's willing to go to extreme lengths in order to ensure their safety and well-being. Whenever he gets especially emotionally involved, his more childish side slips out, which HiMERU describes as being like a childish temper tantrum.

"As his character had been established to have a "Kyoto dialect" for some reason, everyone might have assumed it to be as such, but the way he speaks is one of Akira's creation. I don't know what dialect he is speaking, but if I had to call it something, it would be a "Yakuza dialect". I had believed (?) I was writing him like that from the beginning, so when people responded with stuff like "It surprised me how thick his dialect is!" after I wrote A Dark Night's Passing and such, it actually shocked me." (Akira's Official Works Comment)[12]

Voice line examples here.