This paper presents the designs of injection and suction ducts of co-flow jet (CFJ) flow control airfoils with embedded micro-compressor actuator in cruise condition. The duct cross section outlines are mathematically modeled as superellipse, which has a parameter η to control the outline shape. Several geometry parameters are taken into consideration during the design process, including the shape parameter η, the cross section area of the duct, the semi major axis and semi minor axis of the superellipse. The aerodynamic performance of the ducts are evaluated via numerical simulations, which employ 3D RANS solver with Spalart-Allmaras (S-A) turbulence model, 3th order WENO scheme for the inviscid fluxes, and 2nd order central differencing for the viscous terms. The ducts inlet and outlet shapes are predetermined according to the micro-compressor performance, and the associated boundary conditions are configured based on the 2D simulation results of CFJ airfoils and micro-compressors. The design goal is to eliminate flow separation, maximize the total pressure recovery, and obtain a more uniformly distributed mass flow at the injection duct outlet. The simulation results show that the duct cross section area distribution along the stream wise direction is crucial to control the duct diffusion and flow separation. For the suction duct, the superellipse semi major axis is important to improve the total pressure recovery. For the injection duct, the center body geometry is critical due to the large swirl angle of the flow from the micro-compressor outlet. Moreover, the injection duct guiding vanes can provide a more uniformly distributed mass flow at the duct outlet. Our optimized suction duct presents 99% total pressure recovery. The optimized injection duct shows 95% total pressure recovery without guiding vanes, and shows 93.7% total pressure recovery with guiding vanes.