We consider fluid flow through a layer of adsorbed homopolymer, which we decompose into an equivalent set of polymeric loops, each tethered to the adsorbing wall and obeying Zimm dynamics. Using a multiple scattering analysis, we obtain an integral equation for the velocity profile. New results are presented for flow profiles in steady and oscillatory weak shear past an adsorbed layer at the theta temperature. Near the wall we find a universal behavior under steady shear for the fluid velocity u(z)\ensuremath{\sim}${\mathit{z}}^{\mathit{y}}$ at height z, with an exponent y\ensuremath{\simeq}2.0.