Microfluidic gradient generators are used to study the movement of living cells, lipid vesicles, and colloidal particles in response to spatial variations in their local chemical environment. Such gradient driven motions are often slow (less than 1 μm s⁻¹) and therefore influenced or disrupted by fluid flows accompanying the formation and maintenance of the applied gradient. Even when external flows are carefully eliminated, the solute gradient itself can drive fluid motions due to combinations of gravitational body forces and diffusioosmotic surface forces. Here, we develop a microfluid gradient generator based on the in situ formation of biopolymer membranes and quantify the fluid flows induced by steady solute gradients. The measured velocity profiles agree quantitatively with those predicted by analytical approximations of relevant hydrodynamic models. We discuss how the speed of gradient-driven flows depends on system parameters such as the gradient magnitude, the fluid viscosity, the channel dimensions, and the solute type. These results are useful in identifying and mitigating undesired flows within microfluidic gradient systems.