I think you have to go through the Department of State to get permission. Here is an excerpt from the ATF FAQ's.
ATF Online - Bureau of Alcohol, Tobacco and Firearms(L2) Does a licensee need an export license to export a firearm? [Back]
The GCA does not require export licenses. However, most firearms and ammunition must be exported in accordance with the provisions of the Arms Export Control Act of 1976. Regulations implementing this Act generally require a license to be obtained from the Directorate of Defense Trade Controls, Department of State, PM/DDTC, SA-1, Room 1200, 2401 E St., N.W., Washington, DC 20037; (202) 663-1282.
The export of sporting shotguns and ammunition for sporting shotguns is regulated by the U.S. Department of Commerce rather than the State Department. An export license is generally needed to export these shotguns and ammunition. For further information, contact them at their nearest district office or the Bureau of Industry and Security, Outreach and Educational Services Division, U.S. Department of Commerce, 14th St. & Pennsylvania Ave. N.W., Washington, DC 20230, (202) 482-4811.
When exporting NFA firearms, ATF Form 9 must be completed and approved by ATF prior to export.
[22 U.S.C. 2778, 27 CFR 479.114 and 479.116]