The work aims to study the effects of different parameters on the dynamic stability of flexible electronic multilayer film considering that electronic film requires uniform coating and high overprint lamination accuracy, so as to provide theoretical guidance for the stable transmission of flexible electronic film. The vibration differential equation of the moving multilayer film structure was established by Hamilton’s principle, the discrete equation of state was solved by the implicit Runge-Kutta method, and the corresponding Ω and c1 of the system were calculated according to the Floquet theory. The stable region of the moving multilayer film was larger when the film was simply supported on opposite sides and fixed on opposite sides. In addition, reducing the average speed, tension ratio, non-uniform tension coefficient, and increasing the aspect ratio could improve the stability of the moving multilayer film, and the effect of the average speed change was the most significant. Through the establishment of the mathematical model of the moving flexible electronic multilayer film in actual production, the effect law of different parameters on the dynamic stability of the moving multilayer film is obtained. The research results provide a theoretical basis for stable transmission of flexible electronic multilayer film and improvement of coating uniformity and overprint lamination accuracy.