(Reported to House from the Committee on the Judiciary with amendment, H. Rept. 99-495) Federal Firearms Law Reform Act of 1986 - Amends the Gun Control Act of 1968 to prohibit the transfer or possession of silencers. Permits the interstate sale of rifles and shotguns, provided: (1) the transferee and the transferor meet in person to accomplish the transfer; and (2) the sale, delivery, and receipt comply with the legal conditions of sale in both States. Makes it unlawful for any person to sell or ship any firearm or ammunition to someone who: (1) is under indictment for, or has been convicted of, a felony; (2) is a fugitive from justice; (3) is an unlawful user of or addicted to a controlled substance; (4) has been adjudicated as a mental incompetent or committed to a mental institution; (5) has received a dishonorable discharge from the armed forces; (6) has renounced his U.S. citizenship; or (7) is an illegal alien. Makes it unlawful for such persons to receive, possess, or transfer any firearm or ammunition in interstate or foreign commerce. Permits gun sales at certain gun shows. Prohibits the importation of the barrel of any firearm if the importation of that firearm is prohibited. Revises the criteria reviewed by the Secretary of the Treasury in approving applications for licenses. Grants the Secretary authority to suspend (rather than just revoke) a license. Allows the Secretary to inspect the inventory and records of a licensee to ensure compliance with the recordkeeping requirements of such Act. Modifies the penalty provisions for certain licensee violations. Eliminates the recordkeeping requirements for ammunition sales involving less than 1,000 rounds. Codifies existing regulations requiring reports of multiple firearm sales. Establishes additional mandatory penalties for the use or carrying of firearms or armor-piercing ammunition during certain drug trafficking activities. Imposes additional mandatory penalties for machine gun use in crimes. Limits to felony violations the Government's authority to seize firearms and ammunition. Allows individuals who have violated the Gun Control Act of 1968 or the National Firearms Act to apply for relief from the legal disabilities imposed by such statutes. Authorizes the Secretary to grant such relief. Allows the interstate transport of rifles and shotguns by individuals under certain circumstances. Prohibits the sale, delivery, or transfer of a handgun from a licensed importer, manufacturer, or dealer to an unlicensed individual unless the documentation of the transaction is sent to local law enforcement officers and the Federal Bureau of Investigation.