Flow chemistry presents many advantages over batch processes for the fast and continuous production of polymers under more robust, safer, and easily scalable conditions. Although largely exploited for chain-growth polymerizations, it has rarely been applied to step-growth polymerizations (SGP) due to their inherent limitations. Here, we report the facile and fast preparation of an emerging class of nonisocyanate polyurethanes, i.e., CO2-based poly(oxazolidone)s, by SGP in continuous flow reactors. Importantly, we also demonstrate that functional poly(oxazolidone)s are easily prepared by telescoping a flow module where SGP occurs with reagents able to simultaneously promote two polymer derivatizations in a second module, i.e., dehydration followed by cationic thiol-ene to yield poly(N,S-acetal oxazolidone)s. The functional polymer is produced at a high rate and functionalization degree, without requiring the isolation of any intermediates. This work demonstrates the enormous potential of flow technology for the facile and fast continuous production of functional polymers by SGP.