This paper focuses on the risk of flashover failure along the surface of dielectric films for peaking capacitors and investigates the damage behavior and damage mechanism of polyimide (PI), polypropylene (PP), and polyester (PET) films under the action of higher-amplitude nanosecond pulsed currents. Establishment of a nanosecond pulse current test platform to analyze the performance degradation and structural damage of dielectric films under repeated nanosecond pulse currents by means of flashover voltage monitoring, morphology observation, and chemical characterization. The degradation and damage mechanisms of dielectric film insulation were investigated by varying the flashover channel distance, gas environment, and gas pressure. The damage modes of thin film materials under the action of a flash arc include surface deformation, decreased flash resistance, molecular chain breakage and group detachment. As the number of discharges increased, the flashover withstand voltage of PI was maintained at a more stable value, the flashover voltage of PP showed a slight decrease, and the flashover voltage of PET showed a significant decreasing trend. Combining the differences in the initial along-surface withstand strengths of different films and the changes in flashover voltage under multiple discharges, combined with infrared spectroscopy testing and analysis, we provide experimental and theoretical support for the investigation and risk assessment of the insulation failure mechanism of dielectric films for peaked capacitors.