Porous adsorbents have emerged as leading materials for carbon capture, where pressure-controlled regeneration offers a key advantage over energy-demanding temperature swing adsorption. Flexible metal-organic frameworks (MOFs) comprised of pillared linkers are proposed to meet this need due to the unique ability to adjust their pores to maximize host-guest interactions. However, many pillared MOFs show structural collapse following activation. We highlight a new approach to constructing pillared MOFs which retain their porosity upon activation, while also showing flexibility and selective gas adsorption. Two different MOFs were formed using cubane-1,4-dicarboxylate (cdc) as a pillar linking zinc triazolate sheets, [Zn₂(trz)₂(cdc)] and [Zn₂(trz)₂(Br-cdc)], and their structural framework dynamics investigated using advanced characterization techniques. In situ X-ray powder diffraction performed in parallel with gas adsorption experiments revealed specific, reversible structural transformations between a narrow pore and open pore phase of the MOFs. These new MOFs reveal a high enthalpy of CO₂ adsorption, driven by interesting network flexibility previously unobserved in the collapsed benzene-1,4-dicarboxylate analogue. A combination of experimental techniques and in silico calculations revealed that the phase transformations are governed by local coordination flexibility around the open-metal site available in [Zn₂(trz)₂(cdc)].