Symbolism, Imagery, Allegory
Chin-Kee is clearly a stereotype, or several stereotypes rolled into one character. He's sinister Fu Manchu who wants "'pletty Amellican girl wiff bountiful Amellican bosom'" (3.23); the "model minority" who answers all of the teachers' questions correctly in Danny's classes (6.6-6.19); the geeky, totally oblivious Asian, who doesn't know what a bad singer he is (9.5); and the kung-fu master who's able to do moves like "Spicy Szechuan Dragon," "Mongorian Foot in Face" and "Happy Famiry Head Bonk" (9.22-9.38).
Because all of these things are clearly not what mainstream (white) America imagines itself to be, Chin-Kee is more than just a bunch of stereotypes—he represents the fear of those stereotypes. Specifically, Danny's (or really, Jin's) fear of appearing non-white and non-American.
Wondering how we know this? Just take a look at Danny's facial expressions: they range from cowering embarrassment (6.7) to bug-eyed horror (9.5) whenever he's around Chin-Kee. Moreover, he tries to hide Chin-Kee by bringing him to school late and telling him to "'Stay quiet'" (6.2-6.4), and by dragging him away during Chin-Kee's embarrassing performance of Ricky Martin's "She Bangs" in the library (9.6). Chin-Kee as his "c****y" self forces Danny to constantly confront the fear of being labeled a "c****."
So think of Chin-Kee this way: he symbolizes the threat of stereotypes and the thing that Danny/Jin needs to overcome.