The Second Amendment is about state militias. DC is not a US state so the Second Amendment doesn't apply to DC. That's the clear legal answer to me. But, on a more practical level, there's no Second Amendment reason that a particular type of firearm needs to be legal for anyone to own.
Even if one holds that the introductory clause serves to limit arms access to the militia, the idea that it applies only to the states and not to the territories is absurd. "State" is clearly being used in the 2nd amendment in sense of government in general and not in the sense of one of the constituent polities that make up the United States of America.
Furthermore, in the sense of late 18th century America, as made clear by the drafting history of the amendment, if you were an able-bodied adult citizen, you were part of the militia.