Adsorption-based processes using metal-organic frameworks (MOFs) are a promising option for carbon dioxide (CO2) capture from flue gases and biogas upgrading to biomethane. Here, the adsorption of CO2, methane (CH4), and nitrogen (N2) on Zn(dcpa) MOF (dcpa (2,6-dichlorophenylacetate)) is reported. The characterization of the MOF by powder X-ray diffraction (PXRD), thermogravimetric analysis (TGA), and N2 physisorption at 77 K shows that it is stable up to 650 K, and confirms previous observations suggesting framework flexibility upon exposure to guest molecules. The adsorption equilibrium isotherms of the pure components (CO2, CH4, and N2), measured at 273–323 K, and up to 35 bar, are Langmuirian, except for that of CO2 at 273 K, which exhibits a stepwise shape with hysteresis. The latter is accurately interpreted in terms of the osmotic thermodynamic theory, with further refinement by assuming that the free energy difference between the two metastable structures of Zn(dcpa) is a normally distributed variable due to the existence of different crystal sizes and defects in a real sample. The ideal selectivities of the equimolar mixtures of CO2/N2 and CO2/CH4 at 1 bar and 303 K are 12.8 and 2.9, respectively, which are large enough for Zn(dcpa) to be usable in pressure swing adsorption.