No. Flights into the Flight Restricted Zone (FRZ) cannot be filed electronically using ForeFlight Mobile. To file a flight plan into the DC FRZ, contact the Washington Center Flight Data Unit at 703-771-3476.
You can use ForeFlight Mobile to file a flight plan to an airport in the DC SFRA using the steps in this article:
How do I file an SFRA VFR flight plan inside the DC SFRA?