Flight 800 Improvement Act of 2006 - Directs the Federal Aviation Administration to: (1) finalize and implement, not later than January 1, 2007, a proposed rule relating to the reduction of fuel tank flammability in transport category airplanes; and (2) study and report on ways to improve the safety and reduce the flammability of fuel tanks located on airplane wings. Authorizes the Administrator to provide matching funds to airplane operators and manufacturers for complying with such rule.