You can. It takes a lot of paperwork, but you can. Finding one that can be legally purchased is a challenge, of course. Now, if you want to get something like a G.E. minigun, there are more to pick from on the market.
I'll bet there is a lot of paperwork. Had to do a search for a pic and it had a related link to the Vulcan 20mm. That is a weapon. It stated the Vulcan had been in service since 1959. That is a long time, but awsome. Isn't that what is on board the AC-130H? Gives me chills.