The effect of non-spherical bomb geometry on the evolution of outwardly propagating flames and the determination of laminar flame speeds using the conventional constant-pressure technique is investigated experimentally and theoretically. It is shown that the non-spherical chamber boundary causes significant distortion of the flame surface and modification of the propagation rate through the interaction of the wall and the flow induced by thermal expansion across the flame. The departures from an unconfined case, especially the generation of non-zero burned gas velocities, can lead to significant errors in burning velocities calculated using these conventional assumptions. A flow correction that accounts for the induced flow field is developed and is demonstrated to achieve significant improvements in accuracy for the experimental determination of burning velocity. For atmospheric syngas-air mixtures, the present flow-corrected results are significantly higher than prior reported cylindrical bomb results based upon conventional data interpretation. The flow effect is also shown to influence the determination of the Markstein length significantly. Schlieren images from an experiment with a cuboid combustion chamber reveal that the flame becomes noticeably non-spherical. The outwardly propagating flame to some extent takes the shape of its container - the schlieren images show that the cross-section of a flame traveling into a chamber with a diamond cross-section becomes diamond-shaped itself. This observed flame front distortion further confirms experimentally the effect of flow disturbances caused by the chamber walls on the evolution of outwardly propagating flames.