Most of the acoustic cloak designs are based on the stationary medium, which, however, may be inaccurate in many practical applications with non-uniform flows. The optimization of the acoustic cloaking performance was described as an active noise control problem, and the theoretical model by Huang, Zhong, and Stalnov [J. Acoust. Soc. Am. 135(5), 2571-2580 (2014b)] was employed for the quick evaluation of the sound scattering. In this work, extensions are made to address the unsolved but essential issues in the model. First, the impact of the discontinuities at the interface between the cloak and surrounding fluids is investigated. Second, the high-order Born's approximation is employed to solve the sound governing equation, which can quickly improve the prediction accuracy. Finally, the optimized cloaking strategy is applied to airfoils in turbulent flows to demonstrate the capability of the proposed modelling for cases of practical importance. Also, it is found that the performance of the optimized cloak is insensitive to the frequency of the incident wave. The promising results suggest that an optimized cloaking design can effectively suppress the sound scattering, providing the confidence with the mathematical framework for the potential aeronautics and marine applications.