Research on electronic packaging materials with high electromagnetic interference (EMI) shielding, thermal conductivity, and electrical insulating properties has been flourishing in recent years. In this work, dual three-dimensional (3D) structures of graphene nanoplatelets (GnP) and graphene fluoride (GF) were fabricated in the polydimethylsiloxane (PDMS) composites for electronic packaging materials with superior EMI shielding effectiveness (SE), thermal conductivity, and electrically insulating. The first 3D structure of the porous GnP@PDMS foams was fabricated using the sugar template method. The GF/PDMS solution was then infiltrated into the GnP@PDMS foam by the vacuum infiltration method to create the second 3D network of GF in the GnP@PDMS/GF composites. The prepared porous GnP30@PDMS foam exhibits an EMI SE of 51.26 dB with 30 wt% of GnP. In addition, the introduction of the second 3D network of GF/PDMS plays a vital role to improve the thermal conductivity and electrical insulating properties of the GnP30@PDMS/GF composites. The GnP30@PDMS/GF8 composites showed a thermal conductivity of 1.47 W·m−1·K−1 which is enhanced by 568 % in comparison to the pure PDMS and excellent electrical insulating properties as high as 2.82 × 10−10 S·cm−1 and maintained high EMI SE of 50.13 dB. The extraordinary EMI SE of the GnP@PDMS/GF composites is favorably correlated to the porous interconnected network of GnP while the enhanced thermal conductivity is attributed to the dual 3D thermoconductive channels of GnP and GF. Additionally, the GnP@PDMS/GF8 composites are demonstrated to have outstanding mechanical flexibility, thermal stability, and heat dissipating capability. Therefore, the developed GnP@PDMS/GF composites have great prospects in the field of electronic packaging materials.