I assume that when you say you are "independent" you mean that no one can claim you as a dependent. That has nothing to do with whether or not you have to file Form 8615 ("kiddie tax"). Look at the list that DawnC posted of the conditions for having to file the form. It doesn't say anything about being a dependent or "independent." That's not one of the considerations. If you meet the conditions that DawnC listed, you have to file the form even if you cannot be claimed as a dependent.
