Do you like Kari?

[urban dream]

I'm sorry, but that's flirting. It's the worst kind of flirting, manipulation without affection.

Ah, but who says it was completely without affection? I don't think she's in love with him, but she doesn't dislike Davis either. She obviously likes/respects him as a friend. And besides, that's how teenaged girls are, at least the ones I know... They flirt for fun, not because they're actually in LOVE with everyone they flirt with.
Although, you do have a point, Kari does sort of use him in places. Still, I think she regards him as a friend and not a tool. That's why I don't think her behaviour is malvolent, even though it's not always completely proper.

Maybe it was only in the dub, but I know there were a few occasions where she changed the tone of her voice to ask Daisuke to do her a favor (I can't recall them specifically).

Well, these scenes exist in the German dub as well, so they're probably also present in the Japenese original.