Measurements of anisotropic flow Fourier coefficients (upsilon(n)) for inclusive charged particles and identified hadrons pi(+/-), K-+/-, p, and (p) over bar produced at midrapidity in Cu + Au collisions at root s(NN) = 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 psi(n), for n = 1, 2, and 3 are studied as a function of transverse momentum p(T) 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 root s(NN) and find that the upsilon(2) and upsilon(3), as a function of transverse momentum, follow a common scaling with 1/(epsilon N-n(part)1/3).