It depends on whether you are the custodial parent or not. 

The custodial parent lives with the child more than half of the year, and can use the child to claim head of household filing status (if you meet the requirements) earned income credit, and child and dependent care credit regardless of whether they can claim the child as a dependent on the tax return. (If the father lives with you and the child for the entire year, there are tie-breaker rules to determine who can claim the child and all of the child related tax benefits).

You can only utilize the FSA for dependent care if you are the custodial parent or (if her other parent lives with you and the child) the parent claiming the child as a dependent.