Understanding the flow of a shear-thickening fluid (STF) through a confined geometry is important for developing soft-body armor applications. A real STF exhibits a blend of Newtonian, thinning, and thickening characteristics at viscosity versus shear-rate curve. We analyze the flow characteristics of a real STF using an abstract theoretical model, focusing on fluid dynamics under varying shear rates. The abstract theoretical model employs a combination of different power-law models across various regimes to represent viscosity as a function of varying shear rates. To validate our theoretical model, we compare the analytical results under limiting conditions. We study the effects of stress and strain rate on fluid flow, particularly examining the transitions between the different flow regimes. Our findings indicate that at low shear rates, the Newtonian flow dominates. As the shear rate increases, shear-thinning behavior becomes more prominent, followed by shear-thickening at even higher shear rates. Additionally, we observe that increasing the channel height leads to a transition from Newtonian to shear-thinning flow, with thickening behavior becoming dominant in larger channels.