The parents do NOT file a form 8615 with their return.
Form 8615 is filed with the child's return. It is used to calculate the "Kiddie tax", wherein the tax on a child's investment income (over $2100) is taxed at the parent's tax rate.
If the child's only income is from interest and dividends, Alaska PFD or capital
gains distributions shown on a 1099-DIV, there is a provision for entering
it on the parent's return, instead of the child's. In that case form 8814 is used, not 8615.