No, you would not be able to fly in possession of marijuana. Airlines and airports are under Federal jurisdiction, and marijuana is still illegal under Federal law. TSA agents could let you get by with a warning as they tend to make decisions on a case by case basis. Also there is no instate airline service in Washington D.C. as it is only a few hundred square miles in size.
Marijuana is only legal on DC property for those 21 years and old. Flying involves going through security and the TSA which is a federal agency. Marijuana remains illegal under federal law, so it is highly dangerous to fly. Moreover, DC area airports are not actually on DC property/land.
Under few conditions marijuana is allowed to be taken while flying only if it is for medicinal purposes. But if you are not a proper person to hold marijuana which needs certain license type forms a law enforcement firm will be notified for verifying and since federal law says carrying any kind of marijuana is illegal you have to answer people to get clearance.