The IRS runs the Child and Dependent Care Credit on a calendar basis, without regard to your non-calendar year FSA.
The IRS has dependent FSAs under a "use it or lose" rule. Normally, any FSA funds that were allocate for a certain year but not spent in that year are forfeited (i.e., added back to income).
However, there is the possibility of a run-out period and a grace period being adopted by the employer to allow you to use some FSA funds for a short while into the new year. You should consult with your employer about how your employer handles these plan features. Do it now, because the grace period (if one) probably ends March 15th.
In general, you can't pay in advance for dependent care, you can only declare only those expenses you have actually made.
This means that you can't report that you used FSA funds if you haven't used them yet.
However, you may be able to utilize those expenses next year. When you do your 2018 return, note the screen in the Dependent and Child Care section entitled "Do any of these uncommon situations apply?" (Assuming that next year has the same screens) - here you will find a line "In 2018, we paid for 2017 care expenses that weren't reported in 2016." Here you may be able to utilize the amounts you paid in 2018 for 2017.