For UTMA accounts (Uniform Transfer to Minors), do I have to report my 1099-B?

Yes.  If your minor child's UTMA account has transactions reported on Form 1099-B, they do need to be reported to the IRS.  

However, it will need to be done on your child's own tax return.  You cannot report it on your own return.  Only interest and dividends may be reported on your return for your minor child.