New trends in the circular economy and sustainability are pointing towards the gradual elimination of standard flame retardants such as phosphorus compounds or halogenated compounds. New solutions are therefore being sought in this area and ceramizable composites could be an interesting alternative. Weak rheological properties are one of the main disadvantages of ceramizable composites. This study tested ceramizable composites composed of styrene-butadiene rubber (SBR) as a polymer matrix and mica as a mineral filler and aimed to improve the viscoelastic properties of silicone oil as a plasticizer. To characterize this composite's mechanical properties before and after ceramization, the viscoelastic properties were tested with a dynamic oscillating rheometer and the thermal behavior with a cone calorimeter. This paper also provides results showing differences (via the abovementioned properties) between vulcanization with sulfur and that with peroxide for the ceramizable composites based on SBR. The presented results, showing changes in mechanical properties, dynamic viscosity or flammability, among others, allow a better understanding of elastomeric composites with ceramizable flame-retardant systems. Such composites can find a wide range of applications, from lagging for electrical cables to building elements such as floor coverings and fire barriers.