Flag Protection Act of 1999 - Amends the Federal criminal code to revise provisions regarding desecration of the flag to set penalties with respect to persons who: (1) destroy or damage a U.S. flag with the primary purpose and intent to incite or produce imminent violence or a breach of the peace under circumstances in which the person knows that it is reasonably likely to produce imminent violence or a breach of the peace; (2) steal or knowingly convert to their use, or the use of another, a U.S. flag belonging to the United States and intentionally destroy or damage that flag; and (3) within any lands reserved for the use of the United States, or under the exclusive or concurrent jurisdiction thereof, steal or knowingly convert to their use, or the use of another, a U.S. flag belonging to another person and intentionally destroy or damage that flag.