What special training is required to fly in the Washington DC area?
There is a training course on FAASafety.gov that all pilots operating VFR flight within 60nmi of Washington DC must take.

Since I assume you are flying IFR, you would not be required to take it.

From AOPA:


  All of the following operations are exempt from the training
  requirement:
  
  
  Pilots operating under instrument flight rules (IFR);
  Law enforcement, military, and aeromedical operations; and
  A pilot who must deviate to the extent necessary to address an emergency situation.