  The elliptic flow splitting $\Delta v_2$ between $\bar{u}$ and $u$ quarks as
well as between $\pi^-$ and $\pi^+$ in midcentral Au+Au collisions at
$\sqrt{s_{NN}}=200$ GeV has been studied, based on the framework of an extended
multiphase transport model with the partonic evolution described by the chiral
kinetic equations of motion. Within the available statistics, the slope of
$\Delta v_2$ between $\bar{u}$ and $u$ quarks with respect to the electric
charge asymmetry $A_{ch}$ from the linear fit is found to be negative, due to
the correlation between the velocity and the coordinate in the initial parton
phase-space distribution. Simulations with the magnetic field in QGP
overestimate the splitting of the spin polarization between $\Lambda$ and
$\bar{\Lambda}$ observed experimentally, with the latter more consistent with
results under the magnetic field in vacuum. Considering the uncertainties from
the magnetic field, the quark-antiquark vector interaction, and the
hadronization, as well as the hadronic evolution, our study shows that the
experimentally observed positive slope of $\Delta v_2$ with respect to $A_{ch}$
is not likely due to the chiral magnetic wave.
