In this paper, we consider the generalized stationary Stokes system with $p$-growth and Dini-$operatorname{BMO}$ regular coefficients. The main purpose is to establish pointwise estimates for the shear rate and the associated pressure to such Stokes system in terms of an unconventional nonlinear Havin-Mazya-Wolff type potential of the nonhomogeneous term in the plane. As a consequence, a symmetric gradient $L^{infty}$ estimate is obtained. Moreover, we derive potential estimates for the weak solution to the Stokes system without additional regularity assumptions on the coefficients in higher dimensional space.
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