A sufficient condition of a flat harmonic quasiconformal mapping to be a quasihyperbolic quasi-isometry on any subdomain of C is given in this paper, which generalizes the corresponding results of Euclidean and 1/|ω|2 harmonic mappings. As an application, Schwarz lemma of flat harmonic mapping is also investigated. Besides, properties and constructions of flat harmonic mapping are obtained at the same time.