Measurements of the anisotropic flow coefficients v2{2}, v3{3}, v4{4}, and v4{2} for identified particles (π±, K±, and p + p¯) at midrapidity, obtained relative to the event planes m at forward rapidities in Au + Au collisions at √sNN = 200 GeV, are presented as a function of collision centrality and particle transverse momenta pT . The vn coefficients show characteristic patterns consistent with hydrodynamical expansion of the matter produced in the collisions. For each harmonic n, a modified valence quark-number Nq scaling [plotting vn{m}/(Nq ) n/2 versus transverse kinetic energies (KET )/Nq ] is observed to yield a single curve for all the measured particle species for a broad range of KET . A simultaneous blast-wave model fit to the observed vn{m}(pT ) coefficients and published particle spectra identifies radial flow anisotropies ρn{m} and spatial eccentricities sn{m} at freeze-out. These are generally smaller than the initial-state participant-plane geometric eccentricities εn{PP m } as also observed in the final eccentricity from quantum interferometry measurements with respect to the event plane.