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A novel convolutional autoencoder neural ODE (CAE-NODE) framework is proposed for a reduced-order model (ROM) of transient 2D counterflow flames, as an extension of AE-NODE methods in homogeneous reactive systems to spatially resolved flows. The spatial correlations of the multidimensional fields are extracted by the convolutional layers, allowing CAE to autonomously construct a physically consistent 6D continuous latent manifold by compressing high-fidelity 2D snapshots (256x256 grid, 21 variables) by over 100,000 times. The NODE is subsequently trained to describe the continuous-time dynamics on the non-linear manifold, enabling the prediction of the full temporal evolution of the flames by integrating forward in time from an initial condition. The results demonstrate that the network can accurately capture the entire transient process, including ignition, flame propagation, and the gradual transition to a non-premixed condition, with relative errors less than ~2% for major species. This study, for the first time, highlights the potential of CAE-NODE for surrogate modeling of unsteady dynamics of multi-dimensional reacting flows.