The Compliant foil cylindrical gas film seal is an advanced sealing technology designed for high-speed and high-temperature conditions in a jet engine. Its design involves using a compliant foil to create a cylindrical sealing surface, achieving adaptive sealing in environments with high pressure differences and rotational speeds. For high-speed and high-temperature operation, a speed slip flow model was established by considering film slip flow, wall temperature jump, foil deformation, and gas viscosity-temperature thermal effects. The variations in the lubrication performance of the foil cylindrical gas film seal with changes in shaft misalignment directions, misalignment angles, and operating parameters were investigated. The speed slip leads to a decrease in gas film lift and an increase in leakage. The wall temperature jump phenomenon caused by speed slip leads to a 2.56% decrease in film temperature. The shaft misalignment angles on the high-pressure and low-pressure sides have different impacts on the flow field, with film pressure and temperature differing by 66.78% and 11.19%, respectively.