Context. The chemical inventory of hot Jupiter (HJ) exoplanets atmospheres continue to be observed by various ground and space based instruments in increasing detail and precision. It is expected that some HJs will exhibit strong non-equilibrium chemistry characteristics in their atmospheres, which might be inferred from spectral observations. Aims. We aim to model the three dimensional thermochemical non-equilibrium chemistry in the atmospheres of the HJs WASP-39b and HD 189733b. Methods. We couple a lightweight, reduced chemical network 'mini-chem' that utilises net reaction rate tables to the Exo-FMS General Circulation Model (GCM). We perform GCM models of the exoplanets WASP-39b and HD 189733b as case studies of the coupled mini-chem scheme. The GCM results are then post-processed using the 3D radiative-transfer model gCMCRT to produce transmission and emission spectra to assess the impact of non-equilibrium chemistry on their observable properties. Results. Both simulations show significant departures from chemical equilibrium (CE) due to the dynamical motions of the atmosphere. The spacial distribution of species generally follows closely the dynamical features of the atmosphere rather than the temperature field. Each molecular species exhibits a different quench level in the simulations, also dependent on the latitude of the planet. Major differences are seen in the transmission and emission spectral features between the CE and kinetic models. Conclusions. Our simulations indicate that considering the 3D kinetic chemical structures of HJ atmospheres has an important impact on physical interpretation of observational data. Drawing bulk atmospheric parameters from fitting feature strengths may lead to inaccurate interpretation of chemical conditions in the atmosphere of HJs. Our open source mini-chem module is simple to couple with contemporary HJ GCM models without substantially increasing required computational resources.