This paper presents the influence of selected flame retardant additives on heat release rate and thermokinetics properties of epoxy materials made of epoxy resin—Epidian 5. The epoxy resin underwent flame retardant modification with the use of organophosphorus compounds (Roflam F5, Roflam B7) and Al(OH)3, Mg(OH)2. The fire characteristics of the analysed epoxy resin were determined using the cone calorimeter method, and thermal analysis of epoxy resin and the surface morphology of the analysed epoxy materials was with the use of an SEM microscope with an EDS attachment. The lowest value of the heat release rate was recorded for hardened epoxy resin containing one component additive 5% by weight of Mg(OH)2, as well as two component additive 10% by weight of Roflam F5 and 5% by weight of Al(OH)3. Moreover, the initial temperature of thermal decomposition of phase I of the modified epoxy resin samples with Mg(OH)2 (sample 5M) or organophosphorus compounds and Mg(OH)2 (samples 5B + 10M and 5F + 10M) were higher compared to the unmodified epoxy resin for these samples. Considering the surface morphology of the samples with Mg(OH)2, it can be concluded that the additives cause a homogeneous charred layer.