Hmmm. I usually never do these things, but I'll give it a spin.
Dratini (Dragonite): Vice. The word Vice is synonymous with wickedness, corruption, and sin. I've always thought of Dragonite as a rather vicious Pokemon since first seeing his Gen 1 sprite, and, indeed, with an Adamant nature and a 31 attack IV, this Dragonite promises to be just that.
Slowpoke (Slowking): Murasaki. The Japanese word for the color purple (more specifically, lavender). Now don't count this out just because it's another lame color translation name. This one is particularly appropriate since Slowking's shiny forme is lavender colored. Also, it is usually a feminine name (the most notable example being Murasaki Shikibu, the female author of "The Tale of Genji") and therefore fits the gender. Additionally, purple has connotations in Western traditions with royalty, thus it is a fitting moniker for Slowking. Finally, I find it to be a very beautiful and elegant name, two traits which Slowking could use a little more of (not hating, just saying!).
I really can't come up with anything for Chinchou. I'm sure I could put something down, but I wouldn't like it nearly as much as the two above.