In this study six new s-triazine bishydrazino and bishydrazido-based polymers were synthesized via condensation of bishydrazino s-triazine derivatives with terephthaldehyde or via nucleophilic substitution of dichloro-s-triazine derivatives with terephthalic acid hydrazide. The synthesized polymers were characterized by different techniques. The new polymers displayed good thermal behavior with great values in terms of limited oxygen indexed (LOI) 27.50%, 30.12% for polymers 5b,c (bishydrazino-s-triazine based polymers) and 27.23%, 29.86%, 30.85% for polymers 7a–c (bishydrazido-s-triazine based polymers) at 800 °C. Based on the LOI values, these polymers could be classified as flame retardant and self-extinguishing materials. The thermal results also revealed that the type of substituent groups on the triazine core has a considerable impact on their thermal behavior. Accordingly, the prepared polymers were mixed with ammonium polyphosphate (APP) in different proportions to form an intumescent flame-retardant (IFRs) system and were introduced into polypropylene (PP) to improve the flame-retardancy of the composites. The best results were obtained with a mass ratio of APP: 5a–c or 7a–c of 2:1, according to the vertical burning study (UL-94). In addition, the presence of 25% “weight ratio” of IFR in the composite showed great impact and passed UL-94 V-0 and V-1 tests.