In this paper we study the properties of anisotropic semiconductor quantum dots (QDs) formed in the conduction band in the presence of the magnetic field. The Kane-type model is formulated and is analyzed by using both analytical and finite element techniques. Among other things, we demonstrate that in such quantum dots, the electron spin states in the phonon-induced spin-flip rate can be manipulated with the application of externally applied anisotropic gate potentials. More precisely, such potentials enhance the spin flip rates and reduce the level crossing points to lower quantum dot radii. This happens due to the suppression of the g-factor towards bulk crystal. We conclude that the phonon induced spin-flip rate can be controlled through the application of spin-orbit coupling. Numerical examples are shown to demonstrate these findings.