Spontaneous combustion latency is the initial stage of low-temperature oxidation of coal. This stage provides the original heat for coal spontaneous combustion, which has great research value. However, the oxidation process at this stage is difficult to obtain due to the low oxidation reaction rate of coal in the spontaneous combustion latency. Therefore, we designed a closed oxygen consumption experimental device. This device can realize automatic monitoring and data acquisition of the experimental gas concentration. This device was used to carry out isothermal oxidation experiments on coal at different temperatures and oxidation times. The reaction order and reaction rate constant of the kinetics of the main stage of isothermal oxidation of coal in spontaneous combustion latency are mainly studied. The key active groups that affect the reaction rate constant are discussed by the corresponding Fourier transform infrared spectroscopy experiments. The results show that the reaction order is close to 1 at 30 °C. Then, the reaction order showed an overall downward trend with increasing temperature. The reaction rate constant increases with increasing temperature. As the oxidation times increases, the reaction rate constant decreases gradually, and aliphatic groups show a decreasing trend. Aliphatic structures are key active groups that affect the reaction rate constant during the spontaneous combustion latency. This study helps to improve the understanding of the initial stage of low-temperature oxidation of coal and guide the prevention of coal spontaneous combustion.