A million pounds is believable, but i don't know how much DOD uses per year.
Why is it believable?
Every artillery round uses black powder:
If it's separate loading,( that is 155mm and up), then sewn at the back of the stack of bags of nitrocellulose powder is a red bag of black powder. That is the igniter. At least a couple of ounces by eye, I never weighed one.
If it's semifixed (105mm) then in the middle of that big metal cartridge case there is a pierced tube full of black powder. That is the igniter.
In both cases the primer sets the black powder off and the black powder is what lights the nitrocellulose powder off.
I don't know how tank main gun ammo is constructed. But i suspect there is an igniter in there too.
Not sure about current rocket propellant increments, whether TOW or MLRS or aerial weapons, but I know Honest John (that has been out of the inventory since 1974) had a big black powder igniter.
Black powder is also used for other purposes; For instance illumination shells and ICM have an ejecting charge, and pyrotechnics like smoke rounds have to be lit somehow.