Abstract: The electricity-gas interconnection system plays an important role in enhancing energy efficiency and promoting cleaner energy utilization. As the impact of source-load uncertainty on electricity-gas transmission grows, it is crucial to quantitatively analyze the dynamic energy flow in this interconnected system under uncertainty. This study introduces an affine dynamic energy flow algorithm for the electricity-gas interconnection system based on time-domain embedded. Initially, an affine dynamic energy flow model is established based on uncertainties characterized by affine arithmetic. By embedding the time domain, the affine differential equations are transformed into a recursive computational problem, providing an explicit expression of the affine energy flow concerning time. To address the challenge of noise element superposition in multi-temporal computations and enhance efficiency, a method based on dynamic noise element correction is proposed. This technique yields the distribution of affine dynamic energy flow in continuous time. Simulation results validate the algorithm's ability to quantitatively analyze the transfer of source-load uncertainty over time, showcasing its high accuracy, low conservatism, and computational efficiency.