Two-dimensional covalent organic frameworks (2D COFs) are crystalline polymer networks whose modular 2D structures and permanent porosity motivate efforts to integrate them into sensing, energy storage, and optoelectronic devices. These applications require forming the material as a thin film instead of a microcrystalline powder, which has been achieved previously by including a substrate in the reaction mixture. This approach suffers from two key drawbacks: COF precipitates form concurrently and contaminate the film, and variable monomer and oligomer concentrations during the polymerization provide poor control over film thickness. Here we address these challenges by growing 2D COF thin films under continuous flow conditions. Initially homogeneous monomer solutions polymerize while pumped through heated tubing for a given residence time, after which, they pass over a substrate. When the residence time and conditions are chosen judiciously, 2D COF powders form downstream of the substrate, and the chemical composition of the solution at the substrate remains constant. COF films grown in flow exhibit constant rates of mass deposition, enabling thickness control as well as access to thicker films than are available from previous static growth procedures. Notably, the crystallinity of COF films is observed only at longer residence times, suggesting that oligomeric and polymeric species play an important role in forming the 2D COF lattice. This approach, which we demonstrate for four different frameworks, is both a simple and powerful method to control the formation of COF thin films.