This study evaluates the rheological, mechanical, and cone-calorimeter responses of a flame-retardant polypropylene compound (PP) and its composites containing 10 wt.% glass fibers (PPGF) or melamine fibers (PPMF). Rheological assessments were conducted using oscillatory and capillary rheometry at 190 °C. Mechanical properties were evaluated through tensile, three-point bending, and unnotched Charpy tests, while cone calorimetry was performed in accordance with ISO 5660 at 35 kW/m². All materials demonstrated shear thinning behavior. At low angular frequencies, both fiber-filled systems exhibited higher complex viscosity, storage modulus, and loss modulus compared to PP, with PPMF showing the most substantial increase. The mean tensile strengths were reported as 54.7 MPa for PPMF and 53.2 MPa for PPGF, in contrast to 18.7 MPa for PP. PPGF achieved the highest tensile modulus (6546 MPa), whereas PPMF attained the highest flexural strength (79 MPa), flexural modulus (3648 MPa), and mean unnotched impact strength (44 kJ/m²). On a density-normalized basis, PPMF exhibited superior specific tensile strength and flexural properties, while PPGF maintained the highest specific tensile modulus. Under the tested heat flux, PPMF extended the time to ignition from 68 to 92 seconds and reduced the peak heat release rate from 1010 to 540 kW/m², total heat release from 151 to 94.3 MJ/m², and total smoke release from 1852 to 380 m²/m². PPGF also decreased total heat and smoke release, although its peak heat release rate only reduced to 960 kW/m², and its specific extinction area increased. Within the scope of the reported tests, PPMF offered a more balanced combination of flexural, impact, and cone-calorimeter performance, whereas PPGF exhibited the highest tensile stiffness.