This paper shows that a flame can be an intrinsically unstable acoustic element. The finding is clarified in the framework of an acoustic network model, where the flame is described by an acoustic scattering matrix. The instability of the flame acoustic coupling is shown to become dominating in the limit of no acoustic reflections. This is in contrast to classical standing-wave thermoacoustic modes, which originate from the positive feedback loop between system acoustics and the flame. These findings imply that the effectiveness of passive thermoacoustic damping devices is limited by the intrinsic stability properties of the flame.