Reducing the thermal resistance of thermal interface materials (TIM) is crucial for ensuring efficient thermal management of electronics. Herein, TIMs using the step-by-step cross-link of bio-based epoxy, phosphorus-nitrogen curing agents with furan ring, graphite flakes (GFs), and 4,4’-methylenebis(cyclohexylamine), are demonstrated. Furan rings and GFs serve respectively as conjugated dienes and dienophiles to optimize interface interaction between matrix and fillers via the Diels-Alder reaction. Apart from excellent seamlessly interconnected fillers/matrix interface, phonons are more matched well at heterointerfaces based on the first principles calculation. TIMs showed low interface thermal resistance, fire safety and reprocessability. Moreover, low storage modulus of TIMs could be more conform well to the roughness of mating surfaces. The effective heat conduction capability of TIMs is demonstrated in LED chip cooling, indicating potential thermal management applications in electronic devices. This study provides an effective and facile method for tuning the interfacial thermal conduction of carbon-based thermal management materials without any pretreatments.