Stacked-cup carbon nanotubes (SCCNTs) are generally referred to as carbon nanofibers (CNFs). SCCNTs are much less expensive to fabricate and are regarded as good polymer modifiers suitable for large-scale production. Flexible, SCCNT-based soy lecithin biocomposites were fabricated using liquid natural rubber latex as binder. Natural polymers and the SCCNTs were dispersed in a green solvent using a benchtop high-pressure homogenizer. The inks were simply brush-on painted onto cellulose fiber networks and compacted by a hydraulic press so as to transform into conductive paper-like form. The resulting flexible SCCNT papers demonstrated excellent resistance against severe folding and bending tests, with volume resistivity of about 85 Ω·cm at 20 wt % SCCNT loading. The solvent enabled formation of hydrogen bonding between natural rubber and soy lecithin. Thermomechanical measurements indicated that the biocomposites have good stability below and above glass transition points. Moreover, the SCCNT biocomposites had high through-plane thermal conductivity of 5 W/mK and 2000 kJ/m3K volumetric heat capacity, ideal for thermal interface heat transfer applications.