Polyurethane (PUR), as an engineering polymer, is widely used in many sectors of industries. However, the high fire risks associated with PUR, including the smoke density, a high heat release rate, and the toxicity of combustion products limit its applications in many fields. This paper presents the influence of silsesquioxane fillers, alone and in a synergistic system with halogen-free flame-retardant compounds, on reducing the fire hazard of polyurethane foams. The flammability of PUR composites was determined with the use of a pyrolysis combustion flow calorimeter (PCFC) and a cone calorimeter. The flammability results were supplemented with smoke emission values obtained with the use of a smoke density chamber (SDC) and toxicometric indexes. Toxicometric indexes were determined with the use of an innovative method consisting of a thermo-balance connected to a gas analyzer with the use of a heated transfer line. The obtained test results clearly indicate that the used silsesquioxane compounds, especially in combination with organic phosphorus compounds, reduced the fire risk, as expressed by parameters such as the maximum heat release rate (HRRmax), the total heat release rate (THR), and the maximum smoke density (SDmax). The flame-retardant non-halogen system also reduced the amounts of toxic gases emitted during the decomposition of PUR, especially NOx, HCN, NH3, CO and CO2. According to the literature review, complex studies on the fire hazard of a system of POSS–phosphorus compounds in the PUR matrix have not been published yet. This article presents the complex results of studies, indicating that the POSS–phosphorous compound system can be treated as an alternative to toxic halogen flame-retardant compounds in order to decrease the fire hazard of PUR foam.