Example flexible wall panels (e.g., demising walls) comprising a flexible, thermally insulated multilayer panel with a flammable core has a surprisingly low flame-spread index and smoke-developed index due to the flammable core being sandwiched between two fire resistant pads. The flammable core's high thermal resistance (high R-value) provides most of the panel's thermal insulation while a peripheral compressed region and the fire resistant pads help keep the flammable core from burning. In some examples, the materials and thicknesses of the panel's core, fire resistant pads and surrounding outer skin are such that the panel is of sufficient flexibility to be folded onto itself without experiencing appreciable permanent damage.