Nanoporous carbon-based membranes are very attractive for gas separation due to their interesting combination of high selectivity, permeability, and mechanical strength. Recently, the creation of 2D and 3D porous nanostructures based on the arrangement of 1D sp(3) carbon nanothreads was proposed, characterized by a high specific strength and a narrow pore size distribution. In this study, we use classical Molecular Dynamics simulations to show that planar 2D carbon nanothread-based nanostructures can be used as highly selective membranes for gas separation. Their structural features endow them with high flexibility and the possibility of controlling the characteristic pore diameter upon application of uniaxial tensile strain. Results show that they have mechanical strength superior to those of conventional membranes, and exhibit remarkable strain-dependent selectivities for pairs of gases of interest, being suitable for the development of highly efficient separation processes.