Flowcoating is a popular technique for generating thin (5-200 nm), substrate-supported polymer films. In this process, a reservoir of coating fluid is held between the horizontal substrate and a nearly horizontal blade above the substrate; a film of fluid is drawn out of the reservoir by moving the substrate. Accelerating the substrate produces a film with a thickness gradient, particularly useful for high-throughput measurements where film thickness is an important parameter. The present work compares experimental film thickness profiles with a model based on a Landau-Levich treatment to identify the experimental parameters which govern film thickness. The key parameters are the capillary number and the radius of curvature of the reservoir's static meniscus, which is set by the blade angle, gap height, solution reservoir volume, and contact angles of the fluid with the blade and substrate. The results show excellent quantitative agreement with the first-principles model; the model thus provides a design approach which allows a user to produce polymer thin films of virtually any desired thickness profile.