There is not any registration or qualification with taxing agencies for your entity to be paid from employees flexible spending accounts on either the federal or state level.
In many, if not all, cases the employee will need to pay the cost of child care and be reimbursed by the plan. So, you will need to be prepared to provide receipts acceptable to the employers.
There is not any set of acceptable and unacceptable expenses that will always apply to all plans as each plan can be a bit different at to what are and are not qualified expenses.
One fairly typical example is at https://www.fsafeds.com/fsafeds/summaryofbenefits.asp#EligReimbursementDCFSA
"What expenses are eligible for reimbursement with a DCFSA?
You can use the DCFSA to pay eligible expenses for care of your dependent children under age 13, or for a person of any age whom you claim as a dependent on your federal income tax return and who is mentally or physically incapable of caring for himself or herself.
Examples of eligible services include:
What expenses are NOT eligible for reimbursement by a DCFSA? Examples of ineligible DCFSA expenses include:
*Expenses can only be reimbursed after they have occurred."
There is nothing to do for tax purposes to qualify except to provide the type of care that is eligible and provide proof to the employees for reimbursement.
There may be other health department, or child care services, or other governmental agencies with which you may need to register, qualify, be inspected, take and continue education, etc. for other than tax purposes that I am not addressing.
Please ask if you need more discussion or clarification.