The flexibility of membrane-based carbon capture systems (CCSs) has received considerable attention due to the increasing penetration of intermittent renewable sources. In this paper, a comprehensive techno-economic assessment of several membrane separation processes is performed to investigate the potential and viability of such systems as a flexible CCS technology for integrating into the future low carbon power plants. The technical model involves lumped parameter models for balance of plant and a mechanistic membrane model. The mechanistic membrane model can predict the spatial distributions of species along the membrane length in different flow patterns such as cross and counter-flow. The economic model comprises different cost factors for the capital cost, and operational cost of the system components. The aformentioned models are employed to evaluate four system designs with three membrane types. The impacts of several decision-making parameters such as feed pressure and membrane properties are thoroughly investigated. The results show that considering sweep gas and increasing the feed CO2 concentration lead to lowers required membrane area and energy consumption, respectively. Also, using a high CO2 selectivity membrane leads to lower specific energy, while membranes with a moderate selectivity and high permeability are economically preferable due to a lower required area. Finally, the economic comparison of designs shows that considering feed compression and a counter-current membrane module with sweep gas is the most cost-effective design with a CO2 capture cost of 22.76 $/tCO2. Also, using vacuum pumps is the most energy-efficient design for CO2 capturing, contributing to the flexible operation of the membrane-based CCS.