A method for the synthesis of an amine-containing epoxy resin curing agent by dissolving hexakis-[(4-formyl)phenoxy]cyclotriphosphazene in an excess of isophoronediamine was developed. The curing agent was characterized via NMR and IR spectroscopy and MALDI-TOF mass spectrometry, and its rheological characteristics were studied. Compositions based on DER-354 epoxy resin and the synthesized curing agent with different amounts of phosphazene content were obtained. The rheological characteristics of these compositions were studied, followed by their curing. An improvement in several thermal (DSC), mechanical (compression, tension, and adhesion), and physicochemical (water absorption and water solubility) characteristics, as well as the fire resistance of the obtained materials modified with phosphazene, was observed, compared with unmodified samples. In particular, there was an improvement in adhesive characteristics and fire resistance. Thus, compositions based on a curing agent containing a 30% modifier were shown to fulfill the V-1 fire resistance category. The developed compositions can be processed by contact molding, winding, and resin transfer molding (RTM), and the resulting material is suitable for use in aircraft, automotive products, design applications, and home repairs.