American and Delta have flights from JFK to DC-Reagan National. There are quite a few bus lines that go from NY to DC, see the bus section on this site. Some leave from midtown around Penn Station and some leave from Chinatown. You can also take Amtrak from Penn Station to DC. To get to Penn Station take Airtrain from your terminal to Jamaica Station and transfer to E subway or LIRR to Penn Station. To get to Chinatown, take the J subway from Jamaica to Essex St.
American and Delta have