Many cells display lipid-anchored proteins on their plasma membranes. Fluid flow parallel to the cells may displace these proteins. Examples of this have been observed, but lateral flow transport of membrane proteins has not been widely studied. Measurements of the shear force, membrane friction, and resulting protein velocity will make it possible to determine whether this phenomenon is common and contributes to flow sensing. Our lab has developed a method for measuring flow transport of lipid-anchored proteins in a simplified model system: supported bilayer patches. We show that this method is robust and that the flow mobility observed for lipid-anchored proteins under shear flow depends on the ratio of the hydrodynamic force applied to the protein to the frictional drag provided by the lipid anchor. We show that the expected results are observed when these factors are independently varied. One factor that contributes to membrane drag on lipid-anchored proteins is the interleaflet friction. Interleaflet friction is a fundamental parameter governing membrane mechanics: along with membrane viscosity, it determines the time and energy scales for membrane deformations. However, measurements of this parameter are sparse and have previously been accomplished by a large variety of different experimental techniques, making it difficult to compare them or to identify trends. We adapted a recently developed method to determine how interleaflet friction varies with membrane lipid composition. We show that this method gives reproducible results and can detect changes to interleaflet friction resulting from even small differences in acyl chain structure. In particular, we observe dramatic changes to friction when cholesterol is included in the membrane. We look forward to adapting these techniques to investigate how membrane mechanics impact the mobility of proteins and membranes in living cells.