The onset of surface instability during diffusion-driven swelling of hydrogels depends on the kinetics of the swelling process. Here, we outline a perturbation analysis framework using a finite difference approach for calculating the stability limit of swelling hydrogel plates with graded material properties accounting for kinetic effects. The framework is implemented as a Python routine which is made freely available. Results obtained for bilayered hydrogel plates illustrate that the onset of instability occurs earlier in time and at a lower global swelling ratio when kinetics is accounted for compared to the homogeneous swelling case. This work presents an accessible calculation tool for stability analysis of swelling gels, providing input for the design of novel hydrogel systems.