In 2019, we introduced Flame Retardancy Index (FRI) as a universal dimensionless index for the classification of flame-retardant polymer materials (Polymers, 2019, 11(3), 407). FRI simply takes the peak of Heat Release Rate (pHRR), Total Heat Release (THR), and Time-To-Ignition (ti) from cone calorimetry data and quantifies the flame retardancy performance of polymer composites with respect to the blank polymer (the reference sample) on a logarithmic scale, as of Poor (FRI ˂ 100), Good (100 ≤ FRI ˂ 101), or Excellent (FRI ≥ 101). Although initially applied to categorize thermoplastic composites, the versatility of FRI was later verified upon analyzing several sets of data collected from investigations/reports on thermoset composites. Over four years from the time FRI was introduced, we have adequate proof of FRI reliability for polymer materials ranking in terms of flame retardancy performance. Since the mission of FRI was to roughly classify flame-retardant polymer materials, its simplicity of usage and fast performance quantification were highly valued. Herein, we answered the question “does inclusion of additional cone calorimetry parameters, e.g., the time to pHRR (tp), affect the predictability of FRI?”. In this regard, we defined new variants to evaluate classification capability and variation interval of FRI. We also defined the Flammability Index (FI) based on Pyrolysis Combustion Flow Calorimetry (PCFC) data to invite specialists for analysis of the relationship between the FRI and FI, which may deepen our understanding of the flame retardancy mechanisms of the condensed and gas phases.