This paper presents the split-stencil least square kinetic upwind method for Navier–Stokes (SLKNS) solver using kinetic flux vector splitting (KFVS) scheme with Chapman-Enskog distribution. SLKNS solver operates on an arbitrary distribution of points and uses a novel least squares method which differs from the normal equations approach as it generates the non-symmetric cross-product matrix by selective splitting of the set of neighbours to avoid ill-conditioning. SLKNS also uses the axi-symmetric formulation of the Boltzmann equation and kinetic slip boundary condition. SLKNS is capable of capturing weak secondary flows as well as features of strong rotation characterized by steep density gradient and thin boundary layers towards the peripheral region with a rarefied central core.