In micro-circulatory flow, where the tube diameter exceeds approximately 300µm, fluid flow resistance is quite high when compared to tubes with a diameter smaller than 300µm. Under such circumstances, the transportation of blood flow is further influenced by the Fahraeus-Lindqvist (FL) effect, which introduces variations in viscosity. In this article, we derive a closed-form mathematical expression for fluid flow resistance, taking into account the influence of the FL effect within the context of a circular-shaped artery with rigid, rough walls and a two-layer blood flow configuration. The blood flow within this artery comprises two layers: a central core layer with red blood cells (hematocrit value) and an outer annular layer of plasma. The resulting nonlinear flow resistance is characterized by the influence of wall roughness, hematocrit value, and the viscosity of blood in both layers. Mathematically, it is concluded that the FL effect reduces flow resistance, facilitating blood circulation in micro-capillaries, and this finding holds potential clinical significance.