Three poly(arylene ether ketone)s (PAEKs) with propylidene (C1, C2) and phtalide (C3) fragments, and one phtalide-containing polyarylene (C4), were synthesized. Their chemical structures were confirmed via 1H NMR, 13C NMR and 19F NMR spectroscopy. The polymers have shown a high glass transition temperature (>155 °C), excellent film-forming properties, and a high free volume for this polymer type. The influence of various functional groups in the structure of PAEKs on gas transport parameters was evaluated. Expectedly, due to the higher free volume, the introduction of the hexafluoropropylidene group to PAEK resulted in a higher increase of gas permeability in comparison with the propylidene group. The substitution of the fluorine-containing group on a rigid phtalide moiety (C3) significantly increases the glass transition temperature of the polymer, while the gas permeation slightly decreases. Finally, the removal of two ether groups from the PAEK structure (C4) leads to a rigid polymer chain that is characterized by the highest free volume, gas permeability, and diffusion coefficients among the PAEKs under investigation. Also, theoretically predicted transport parameters were investigated, to further study the structure–properties relationship for the PAEKs. Methods of modified atomic (MAC) and bond (BC) contributions were applied for this purpose (estimation of gas permeation and diffusion). Gas solubility coefficients for PAEKs were forecasted by the “Short polymer chain surface based prediction” (SPCSBP) method. Both the MAC and BC techniques showed reasonable predicted parameters for three polymers, while a significant underestimation of gas transport parameters was observed for C4. The results for all three prediction methods were compared with the experimental data obtained in this work. The predicted parameters were in good agreement with the experimental data for phtalide-containing polymers (C3 and C4), while for propylidene-containing poly(arylene ether ketone)s they were overestimated, due to a possible influence of the propylidene fragment on the indices of the oligomeric chains. MAC and BC methods demonstrated a better prediction power than the SPCSBP method.