Conducting polymerizations under continuous flow conditions affords distinct advantages over batch experimentation and has increasingly been employed by the research community for chain-growth polymerizations to accelerate materials discovery and to finely tune material properties. Our work now expands on the reported advances by demonstrating the utility of continuous flow for polyaddition reactions of polyurethanes (PUs). Various reactor configurations enable the on-demand organocatalytic synthesis of linear polyurethanes with tailored soft to hard segment ratios and under residence times of 3-5 min at room temperature. Implementing in-line analytics for real-time process monitoring increases the control over monomer conversion and minimizes batch-to-batch variations. Theoretical and experimentally determined molecular weights and material compositions were in good agreement and demonstrate reliability and reproducibility of the processes. Thus, these systems enable the straightforward preparation of libraries of commercially relevant PU materials and we demonstrate how the glass transition temperature can be modulated by composition. Finally, we discuss developed process control mechanisms aiming at increasing process automation and the underlying challenges due to employing reactive solutions.