Theory of formerly proposed "flight time integral method" for the rigorous analyses of transport property of charged particles in gas under electric and magnetic fields is derived using the path integral formulation of the Boltzmann equation. Fundamental formulae in the FTI procedure to obtain the velocity distribution and transport coefficients are presented in comparison with those of the path integral method. Under arbitrary conditions of fields and cross sections, this method is quite stable and accurate, due to the procedure based on the normalized starting rate distribution from which the flight behavior is calculated through the time.