In order to deploy machine learning in a real-world self-driving laboratory where data acquisition is costly and there are multiple competing design criteria, systems need to be able to intelligently sample while balancing performance tradeoffs and constraints. For these reasons, we present an active learning process based on multiobjective blackbox optimization with continuously-updated machine learning models. This workflow is built upon open-source technologies for real-time data streaming and modular multiobjective optimization software development. We demonstrate a proof-of-concept for this workflow through the autonomous operation of a continuous-flow chemistry laboratory, which identifies ideal manufacturing conditions for the electrolyte 2,2,2-trifluoroethyl Methyl carbonate.