Adsorbed natural gas (ANG) technology is a viable alternative to conventional liquefied or compressed natural-gas storage. Many different porous materials have been considered for adsorptive, reversible methane storage, but fall short of the US Department of Energy targets (0.5 g g−1, 263 l l−1). Here, we prepare a flexible porous polymer, made from benzene and 1,2-dichloroethane in kilogram batches, that has a high methane working capacity of 0.625 g g−1 and 294 l l−1 when cycled between 5 and 100 bar pressure. We suggest that the flexibility provides rapid desorption and thermal management, while the hydrophobicity and the nature of the covalently bonded framework allow the material to tolerate harsh conditions. The polymer also shows an adsorbate memory effect, where a less adsorptive gas (N2) follows the isotherm profile of a high-capacity adsorbate (CO2), which is attributed to the thermal expansion caused by the adsorption enthalpy. The high methane capacity and memory effect make flexible porous polymers promising candidates for ANG technology.