  The individual studies of the anisotropic flow vector, flow angle and flow
magnitude fluctuations with multi-particle correlations provide insight into
the initial conditions and properties of the quark-gluon plasma (QGP) created
in high-energy heavy-ion collisions. Recent measurements of these fluctuations
have been available and the comparison to hydrodynamic models shows unique
sensitivities to the initial conditions of the system, but also a puzzling
dependence on the specific shear viscosity $\eta/s$. In this paper, a
systematic study with A Multi-Phase Transport (AMPT) model using different
tunings of the initial conditions, partonic cross section and hadronic
interactions investigates the $p_{\rm T}$-dependent flow vector, flow angle and
flow magnitude fluctuations. It is found that the transport model reasonably
describes the flow vector, flow angle and flow magnitude fluctuations observed
in data and that the fluctuations are driven by fluctuations in the initial
state. The comparison of data and model presented in this paper enables further
constraints on the initial conditions of the heavy-ion collisions.
