Measurements of anisotropic flow Fourier coefficients (vn) for inclusive charged particles and identified hadrons π±, K±, p, and p produced at midrapidity in Cu+Au collisions at sNN=200 GeV are presented. The data were collected in 2012 by the PHENIX experiment at the Relativistic Heavy-Ion Collider (RHIC). The particle azimuthal distributions with respect to different-order symmetry planes Ψn, for n=1, 2, and 3 are studied as a function of transverse momentum pT over a broad range of collision centralities. Mass ordering, as expected from hydrodynamic flow, is observed for all three harmonics. The charged-particle results are compared with hydrodynamical and transport model calculations. We also compare these Cu+Au results with those in Cu+Cu and Au+Au collisions at the same sNN and find that the v2 and v3, as a function of transverse momentum, follow a common scaling with 1/(nNpart1/3).