Recent studies on applications of the lattice Boltzmann method (LBM) and the finite-difference lattice Boltzmann method (FDLBM) to velocity slip simulations are mostly on one-dimensional (1D) problems such as a shear flow between parallel plates. Applications to a 2D problem may raise new issues. The author performed numerical simulations of rotational slip flow in coaxial cylinders as an example of 2D problem. Two types of 2D models were used. The first were multi-speed FDLBM models proposed by the author. The second was a standard LBM, the D2Q9 model. The simulations were performed applying a finite difference scheme to both the models. The study had two objectives. The first was to investigate the accuracies of LBM and FDLBM on applications to rotational slip flow. The second was to obtain an experience on application of the cylindrical coordinate system. The FDLBM model with 8 directions and the D2Q9 model showed an anisotropic flow pattern when the relaxation time constant or the Knudsen number was large. The FDLBM model with 24 directions showed accurate results even at large Knudsen numbers.