Flexibility in power plants with amine based carbon dioxide (CO₂) capture is widely recognised as a way of improving power plant revenues. Despite the prior art, its value as a way to improve power plant revenues is still unclear. Most studies are based on simplifying assumptions about the capabilities of power plants to operate at part load and to regenerate additional solvent after interim storage of solvent. This work addresses this gap by examining the operational flexibility of supercritical coal power plants with amine based CO₂ capture, using a rigorous fully integrated model. The part-load performance with capture and with additional solvent regeneration, of two coal-fired supercritical power plant configurations designed for base load operation with capture, and with the ability to fully bypass capture, is reported. With advanced integration options configuration, including boiler sliding pressure control, uncontrolled steam extraction with a floating crossover pressure, constant stripper pressure operation and compressor inlet guide vanes, a significant reduction of the electricity output penalty at part load is observed. For instance at 50% fuel input and 90% capture, the electricity output penalty reduces from 458 kWh/tCO₂ (with conventional integration options) to 345 kWh/tCO₂ (with advanced integration options), compared to a reduction from 361 kWh/tCO₂ to 342 kWh/tCO₂ at 100% fuel input and 90% capture. However, advanced integration options allow for additional solvent regeneration to a lower magnitude than conventional integration options. The latter can maintain CO₂ flow export within 10% of maximum flow across 30-78% of MCR (maximum continuous rating). For this configuration, one hour of interim solvent storage at 100% MCR is evaluated to be optimally regenerated in 4 h at 55% MCR, and 3 h at 30% MCR, providing rigorously validated useful guidelines for the increasing number of techno-economic studies on power plant flexibility, and CO₂ flow profiles for further studies on integrated CO₂ networks.