The chiral magnetic wave (CMW) has been theorized to propagate in the Quark-Gluon Plasma formed in high-energy heavy-ion collisions. It could cause a finite electric quadrupole moment of the collision system, and may be observed as a dependence of elliptic flow, v(2), on the asymmetry between positively and negatively charged hadrons, A(ch). However, non-CMW mechanisms, such as local charge conservation (LCC) and hydrodynamics with isospin effect, could also contribute to the experimental observations. Here we present the STAR measurements of elliptic flow v(2) and triangular flow v(3) of charged pions, along with v(2) of charged kaons and protons, as functions of A(ch) in Au+Au collisions root S-NN = 200 GeV. The slope parameters of Delta v(2)(A(ch)) and Delta v(3)(Ach) are reported and compared to investigate the LCC background. The similarity between pion and kaon slopes suggests that the hydrodynamics is not the dominant mechanism. The difference between the normalized Delta v(2) and Delta v(3) slopes, together with the small slopes in p+Au and d+Au collisions at root S-NN = 200 GeV, suggest that the CMW picture remains a viable interpretation at RHIC.