Polymeric integrated Young interferometer sensor chips utilizing a slot waveguide have demonstrated to be sensitive, to work at visible wavelengths, to be manufacturable by simple process, and to have a reduced sensitivity to temperature fluctuations. Although slot waveguide Young interferometers have these desirable features for low-cost rapid diagnostics, the sensor readout is disturbed by mechanical drifts of the sensing system. In this paper we demonstrate that mechanical drifts of the readout system can be compensated by using a multichannel slot waveguide Young interferometer having two reference waveguides and applying a drift compensation method based on the analysis of the spatial shifts of the interferogram fringes. The applicability of the drift compensation method was studied by conducting experiments with undisturbed and with mechanically disturbed setup to measure the phase changes induced by the changes of the bulk refractive index. By applying the drift compensation method, the sample induced phase change responses were extracted from up to 18 times larger measured phase changes in the disturbed experiments proving the applicability of the method with multichannel slot waveguide Young interferometers.