Extrusion based Additive manufacturing (AM) has evolved as an effective way for 3D printing of composites. The flexibility to use wide range of polymers and large size part printing popularizes the process. Extrusion based AM overcomes the issue of filament buckling in flexible part printing during conventional Fused Filament Fabrication process. This work deals with printing of flexible electrically conductive polymer composite parts on a CNC milling machine through a customized material extrusion tool. The samples were printed on a detachable heating bed placed on the CNC milling machine setup. Ethylene Vinyl Acetate (EVA) and Polymer composite of EVA with graphene has been used directly in pellet form. Graphene in the form of filler has been added in 2.5%, 5%, 7.5% and 10% by weight in the composite by melt mixing process. The resistivity of the composite reduces by 79%, (from 592.8 Ω-cm to 121.98 Ω-cm) when filler concentration is changed from 2.5% to 10%. The flow behavior of EVA and its composite was studied through rheological analysis and the microstructural analysis ensured the presence of graphene flakes in EVA graphene composite. Field Emission Scanning Electron microscopy and Energy dispersive spectroscopy ensured the presence and homogeneous dispersion of graphene flakes in the polymer composite made. The application of flexible and flexible conductive parts lies in fabrication of electronic components, sensors, displays, solar cells, flexible antenna and wearable health monitoring devices.