Combustion measurements, such as heat release rate, critical flux, time-to-ignition, ignition temperature, thermal inertia, and kinematics—activation energy as well as preexponential factor—on epoxy polymer (Prime™20LV) with expandable graphite (EG) inorganic filler of different weight percentage composites, are conducted using the Dual Cone Calorimeter, the thermogravimetric analysis (TGA), and Linseis (Germany) THB100 Transient Hot Bridge thermal conductivity analyser. The results indicate that increasing the amount of EG in polymer composite leads to reduction in the critical flux, the time-to-ignition, the ignition temperature, the thermal inertia, the average thermal conductivity, and the activation energy (from 159.1 ± 2.3 to 145.9 ± 3.1 kJ/mol for neat epoxy to 3 wt.% EG-epoxy) of the composite samples. There is, however, an increase in the heat of gasification with increasing EG content.