Normally, the recovery effect of a heavy-oil reservoir gradually deteriorates after multiple rounds of cyclic steam stimulation (CSS). However, the injection of flue gas can effectively increase the utilization degree of steam heat energy, which improves the recovery effect. In this paper, an experimental method for CSS using an energy storage container was established. Based on this method, a one-dimensional core physical simulation experiment for CSS under different flue gas ratios was performed. During the experiment, the changes in temperature field, oil production rate, increase in backpressure, and oil recovery factors were tested. In addition, differences in these data under different injection steam-flue gas ratios were compared. The results show that the flue gas provides a channel of fluids in porous media for steam, which is conducive to the heat transfer of steam to the deeper part of the sandpack. The sandpack has a higher temperature in each cycle than the CSS. The core temperature of each round of flue-gas-assisted CSS is higher than that of the CSS. The final oil recovery factors of flue-gas-assisted CSS using different steam-flue gas ratios are 22.2, 26.7, 30.8, 24.4, and 21.6%, while that of CSS is only 17.2%. According to the experiment, it is concluded that the best steam-flue gas ratio to optimize the flue-gas-assisted CSS is 1:10. With the combined effect of three factors (the temperature field of the sandpack, energizing effect of the flue gas, and degree of oil during recovery), the flue-gas-assisted CSS using the steam-flue gas ratio of 1:10 maximizes the steam heat transfer, increases the energy of return discharge, replenishes formation energy, and improves the oil recovery factor. Through the experiment, the research results provide theoretical guidance for improving the effectiveness of the CSS of heavy-oil reservoirs.