Protein hydrogel-based microchips are being developed for high-throughput evaluation of the concentrations and activities of various proteins. To shorten the time of analysis, the reaction-diffusion kinetics on gel microchips should be accelerated. Here we present the results of the experimental and theoretical analysis of the reaction-diffusion kinetics enforced by mixing with peristaltic pump. The experiments were carried out on gel-based protein microchips with immobilized antibodies under the conditions utilized for on-chip immunoassay. The dependence of fluorescence signals at saturation and corresponding saturation times on the concentrations of immobilized antibodies and antigen in solution proved to be in good agreement with theoretical predictions. It is shown that the enhancement of transport with peristaltic pump results in more than five-fold acceleration of binding kinetics. Our results suggest useful criteria for the optimal conditions for assays on gel microchips to balance high sensitivity and rapid fluorescence saturation kinetics.