Biomimicry involves drawing inspiration from nature's designs to create efficient systems. For instance, the unique herringbone riblet pattern found in bird feathers has proven effective to minimize drag. While attempts have been made to replicate this pattern on structures like plates and aerofoils, there has been a lack of comprehensive optimization of their overall design and of their constituent individual repeating structures. This study attempts to enhance the performance of individual components within the herringbone riblet pattern by leveraging computational fluid dynamics (CFD) and supervised machine learning to reduce drag. The paper outlines a systematic process involving the creation of 107 designs, parameterization, feature selection, generating targets using CFD simulations, and employing regression algorithms. From CFD calculations, the drag coefficients (Cd) for these designs are found, which serve as an input to train supervised learning models. Using the trained transformed target regressor model as a substitute to CFD, Cd values for 10,000 more randomly generated herringbone riblet designs are predicted. The design with the lowest predicted Cd is the optimized design. Notably, the regressed model exhibited an average prediction error rate of 6% on the testing data. The prediction of Cd for the optimized design demonstrated an error of 4% compared to its actual Cd value calculated through CFD. The study also delves into the mechanics of drag reduction in herringbone riblet structures. The resulting optimized microstructure design holds the potential for reducing drag in various applications such as aerospace, automotive, and marine crafts by integrating it onto their surfaces. This innovative approach could significantly transform drag reduction and open pathways to more efficient transportation systems.