I can’t buy a military assault rifle. Neither can you, at least legally.
Well you actually could buy an automatic weapon if it was manufactured prior to 1986. It would have to be one registered with the BATF in the National Firearms Registration and Transfer Records. You would have to find an FFL dealer who has gone through additional background checks and paid additional fees. These are called Class 3 FFL dealers and they go through extensive investigation by the ATF.
Then if you find the automatic assault weapon you want, you have to pay a $200 tax and register a 12 page application, submitting fingerprints and photos to the ATF. Good luck getting approval but you can certainly try. The average wait time for approval, if you get it, is nine months. Your name and address will be registered with your local police and if you want to cross state lines with your new purchase you will have to apply for permission.