We describe theoretically the flow of a good solvent through two closely spaced polymer brushes. The brushes expand in response to the shear flow and decrease the cross-sectional area for flow. As such, this assembly of polymer chains acts as both sensor and valve for microflow control and bypasses the need to construct an external feedback mechanism. The discharge through the brush-linked conduit is a nonlinear function of pressure, enabling different modes of valve operation. For brushes which extend moderately into the interslit region, the valve assembly maintains constant discharge over a wide range of pressure. For brushes which extend far into the interslit region, the valve assembly cuts off flow above a critical pressure, limiting the maximum discharge.