Gun Trafficking Prohibition Act This bill establishes stand-alone criminal offenses for trafficking in firearms and straw purchasing of firearms. The bill expands the categories of prohibited persons (i.e., persons barred from receiving or possessing a firearm or ammunition) to include persons who intend (1) to sell or transfer a firearm or ammunition to a prohibited person, (2) to sell or transfer a firearm to further a crime of violence or drug trafficking offense, or (3) to unlawfully export. It increases the maximum prison term for the (1) sale or transfer of a firearm to a prohibited person, or (2) receipt or possession of a firearm by a prohibited person. The bill revises the existing prohibition on transferring a firearm knowing that it will be used to commit a crime of violence or drug trafficking offense. Specifically, it broadens the scope of unlawful conduct covered by the prohibition and increases the maximum prison term for a violator. Similarly, the bill revises the existing prohibition on smuggling a firearm into the United States with the intent to unlawfully import or to promote a crime of violence or drug trafficking offense. It broadens the scope of unlawful conduct and increases the maximum prison term for a violator. Finally, the bill makes it a crime to smuggle a firearm or ammunition out of the United States, or conspire or attempt to do so, with the intent to unlawfully export or to promote a crime of violence or drug trafficking offense.