Income earned in Loved accounts for your children are tax-free up to $1,050 of income per year per child.
For earnings above $1,050, the next $1,050 is taxed at the child's tax rate and any remaining income is then taxed at their parent's tax rate.
These rules apply to accounts for children under age 19 and full-time college students under the age of 24.
A parent can avoid having to fill a tax return for their child by including the income on their own tax return, however different tax rules will apply depending on your circumstances.
For my information on children taxes, please see https://www.irs.gov/taxtopics/tc553