However this checking account has my child name as a secondary holder and I am as the primary holder. I am thinking if the checking account has my child as the primary holder then I would get box 6 unchecked. Is my thinking is correct?
The distributions should be made by the beneficiary only in order to be applied to education expenses. Funds can also be directly transferred to the school. The IRS has not been enforcing this rule, but you can ask the financial institution to correct the 1099-Q.
Yes, you should keep records to show that the distribution was made on the beneficiary's behalf and used to pay education expenses in case the IRS ever questions it.
Please read IRS Pub. 970 for information and ideas on how to maximize your tax breaks for education.