3D bioprinting technology has promising applications in regenerative medicine and drug testing in the near future for the fabrication of patient-specific replicas of human organs, bones, etc. Previously, we have developed a dual-arm 3D bioprinting system, TwinPrint, using two robots to cooperatively bioprint peptide-based soft matter structures. During 3D bioprinting, optimization of extrusion flow rates of peptide bioinks is critical for efficient cell encapsulation and mechanical stability. Currently, it is dependent on user knowledge and experience from past experiments which may vary in reliability and quality. Thus, this paper proposes a multi-output regression machine learning model to predict optimized peptide flow rates for the microfluidic-based pumping component of the TwinPrint system. Specifically, parameters including peptide bioink type, peptide concentration, phosphate-buffered saline (PBS) concentration and nozzle size are used as inputs for machine learning methods. The output is estimated optimal flow rates of the bioink fluid components, essential in obtaining a consistent amount of gel extrusion. The dataset used to train and test the predictive model is collected from numerous bioprinting experiments conducted on-site. Performance evaluation metrics are applied to examine and assess the developed model, which is incorporated within our in-house developed TwinPrint software to automatically suggest flow rates once the user specifies initial parameters. Finally, the flow rate predictive software in conjunction with the advanced dual-arm robotic system hardware are demonstrated in this work to pave the way for automated optimization of 3D bioprinting for enhanced printability, repeatability and standardization.