Graphene nanoplatelets (GNPs) were dispersed in poly(butylene adipate-co-terephthalate) (PBAT) by melt mixing. Morphological studies were carried out via scanning electron microscopy and X-ray diffraction. Results showed good dispersion of GNPs in PBAT at low filler loadings. SEM images showed establishment of physical contact between GNPs above 9 wt% which was also detected in electrical conductivity measurements where a sharper increase in conductivity was observed beyond this GNP loading. Interestingly, thermal stability of PBAT was also found to enhance as the GNP loading was raised to 9 wt% and higher. Melt flow behaviours of the prepared nanocomposites were characterized by dynamic and steady shear rate tests. Viscoelastic properties exhibited significant enhancement with increasing GNP loading. The effect of GNPs was more pronounced in storage modulus which exhibited less frequency dependency in the low frequency region. Rheological percolation threshold of GNPs in PBAT was determined to be in vicinity of 9 wt% at 140 °C which is in good agreement with SEM and electrical conductivity results. However, percolation was found to be temperature sensitive, occurring at lower GNP concentrations as the temperature was increased further from the system’s melting point.