Yes, you are still eligible to claim the Child Care Credit for part of your out of pocket Child Care Expenses. The maximum eligible Child Care Expense allowed per child is $3,000.
So for example, if you have one child, $1,800 of your Child Care Expenses will be used to calculate the Child Care Credit on Form 2441 [$3,000 limit per child - $1,200 FSA = $1,800].
See the TurboTax FAQ for more details about getting the Child Care Credit below:
https://ttlc.intuit.com/replies/4395614