A "kinch" refers to the blade of a knife. This is Mulligan's nickname for Stephen Dedalus, the main character in the first three episodes of Ulysses. Dedalus first appeared in Joyce's A Portrait of the Artist as a Young Man. Dedalus is now several years older and a teacher. Like the younger version of himself, Dedalus is still proud and poor, but he has not managed to rise to the artistic heights he prophesied at the end of Portrait.
The nickname is fitting (Dedalus is "sharp" in terms of his intellect, observations, and personality), but the nickname is mocking as well (Dedalus is "dull" in terms of social skills and ambition).
