Molecular dynamics (MD) and Monte Carlo (MC) simulations were used to study the structural and gas transport properties of a group of three highly permeable glassy polyamides containing phosphaphenanthrene skeleton and substituted triphenylamine side groups. The polymer chains were relaxed using a combination of canonical and isothermal-isobaric ensemble simulations to obtain the final equilibrium density. The grand canonical Monte Carlo method coupled with a canonical MD simulation was used to study the solubility of small gases in these polymers. The accuracy of the methods used in this work was tested and validated by comparing the physical and gas transport properties of gases with the available experimental data. The presence of large bulky side groups along the rigid backbone of the polymer, hinders its efficient packing and results in a superior free volume distribution. The computed diffusivities and solubilities of gases are significantly higher for the poly-amides containing both phosphaphenanthrene and trityl-substituted triphenylamine side groups. The thermal motion of the gases, which results in frequent jumps from one free volume region to another, is enhanced with the availability of larger cavities. These molecular details can provide critical information for the experimental design of highly selective and efficient gas separation membranes.