We investigated the effect of the type and amount of expandable graphite (EG) and blackcurrant pomace (BCP) on the flammability, thermal stability, mechanical properties, physical, and chemical structure of viscoelastic polyurethane foams (VEF). For this purpose, the polyurethane foams containing EG, BCP, and EG with BCP were obtained. The content of EG varied in the range of 3–15 per hundred polyols (php), while the BCP content was 30 php. Based on the obtained results, it was found that the additional introduction of BCPs into EG-containing composites allows for an additive effect in improving the functional properties of viscoelastic polyurethane foams. As a result, the composite containing 30 php of BCP and 15 php of EG with the largest particle size and expanded volume shows the largest change in the studied parameters (hardness (H) = 2.65 kPa (+16.2%), limiting oxygen index (LOI) = 26% (+44.4%), and peak heat release rate (pHRR) = 15.5 kW/m² (−87.4%)). In addition, this composite was characterized by the highest char yield (m₆₀₀ = 17.9% (+44.1%)). In turn, the change in mechanical properties is related to a change in the physical and chemical structure of the foams as indicated by scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) analysis.