In the first part of this work, novel elastomeric panels with paraffin for thermal energy storage applications were developed. Ethylene-Propylene Diene Monomer (EPDM) rubber filled with a shape-stabilized paraffin, as phase change material with a melting temperature of 28 °C, was covered with a nitrile-butadiene rubber (NBR) envelope. In order to improve the fire resistance, two selected flame retardants (FRs) were dispersed both in the EPDM core and in the NBR envelope. In this work, the combustion residues from cone calorimeter tests were analysed by various techniques to explain the combustion mechanisms and the interaction of FRs. Nuclear magnetic resonance (NMR) evidenced the complexity of the system, characterized by the formation of char, by the reactivity of organomodified montmorillonite (oMMT) in presence of phosphates and structural rearrangements of the inorganic components. The use of a flame retardant based on ammonium polyphosphate and synergistic agents (based on phosphorus) led to formation of different Al-O-P and Si-O-P compounds. The X-ray diffraction (XRD) analysis highlighted that the formation of silicon phosphate, from the reaction of ammonium polyphosphate and oMMT, was possible only at high phosphorus contents. From the phosphorus content detected through energy dispersive X-ray spectroscopy (EDX) it was possible to indicate that the phosphorus remained in the condensed phase during the combustion.