A combustion chemistry acceleration scheme is developed based on deep operator networks (DeepONets). The scheme is based on the identification of combustion reaction dynamics through a modified DeepOnet architecture such that the solutions of thermochemical scalars are projected to new solutions in small and flexible time increments. The approach is designed to efficiently implement chemistry acceleration without the need for computationally expensive integration of stiff chemistry. An additional framework of latent-space dynamics identification with modified DeepOnet is also proposed which enhances the computational efficiency and widens the applicability of the proposed scheme. The scheme is demonstrated on simple chemical kinetics of hydrogen oxidation to more complex chemical kinetics of n-dodecane high- and low-temperature oxidations. The proposed framework accurately learns the chemical kinetics and efficiently reproduces species and temperature temporal profiles corresponding to each application. In addition, a very large speed-up with a great extrapolation capability is also observed with the proposed scheme.