You can, but you will probably sound quite vapid and ridiculous, like the kind of people that talk like that in the US. "That girl's throwing up" is just as effective, without using the graphic and revolting alternative "chunk," better left for kids in third grade and stoners.

I don't recommend saying that at all.

thank you very much

If you mean a chicken, you'd say "the chicken is clucking". A chick is a baby chicken (as well as a young girl), so the sound for a baby chicken is "chirping". Most small birds chirp.