We report a new insulation composite of aramid honeycombs filled with superflexible resorcinol–formaldehyde aerogels. Aerogels produced via a sol–gel process were dried with supercritical CO2. The aerogels exhibit a high, rubber-like flexibility, due to almost zero shrinkage and networking of nanoparticles and suitably sized macropores. The high porosity of the aerogels in the range of about 95–98% leads to a low thermal conductivity about 0.037 W/mK and low bulk density of 0.05 g/cm3. The filling of light and stiff aramid honeycombs with these flexible aerogels results in a composite with decreased thermal conductivity and modified mechanical properties.