Kittens vomiting incompletely digested food may be caused by indigestion, improper diet, food accumulation, gastrointestinal diseases, or internal parasites. You need to observe the kitten's mental state first. If the kitten appears to be mentally ill , diarrhea and other conditions, it is best to send the kitten to a pet hospital for examination and treatment; if the kitten has no abnormality, it can be fed some probiotics for conditioning.