Once you find a FFL (licenced gun seller) with an export licence, you have a lot of paperwork ahead of you. This from the ATF.

To export firearms other than sporting
shotguns or ammunition for firearms other
than sporting shotguns, the FFL from whom
you purchase the firearm/ammunition must be
registered with the Department of State, Office
of Defense Trade Controls (ODTC). The FFL
must obtain an export license from the ODTC
prior to exportation.

❖ The State Department recommends that
you provide the FFL with a letter from your
embassy on embassy letterhead explaining
why you want to export the firearm/
ammunition. You also should provide an
import authorization issued by the competent
Government office in your country.