Electricity generation from renewable energy sources is emerging as a result of global carbon emission reduction policies. However, most renewable energy sources are non-dispatchable and cannot be adjusted to meet the fluctuating electricity demands of society. A flexible operation process has been proposed as an effective solution to compensate for the unstable nature of renewable energy sources. Thermal load fluctuations during flexible operation may cause creep-fatigue damage to the high-temperature components of thermal power plants, as they are designed with a focus on creep damage under a constant power level. This study investigated the residual life of high-temperature components, such as a superheater tube and a reheater header, to failure under flexible operation conditions using finite element analysis and empirical models. First, we determine an analytical solution for the straightened superheater tube under thermal conditions and compare it with the numerical solution to verify the numerical models. Through the verified finite element model, the creep-fatigue life of the reheater header is estimated by considering flexible operation factors and employing the Coffin-Manson and Larson-Miller models. Although fatigue damage increases with decreasing minimum load and ramp rate, we confirmed that creep damage significantly affects the residual life during flexible operation. In addition, a surrogate model was proposed to evaluate the residual life of the reheater as a function of the flexible operation factors using the machine learning methodology, based on the results of finite element methods. It can be used to predict its residual life without performing complex thermal-structure analysis and relying on empirical models for fatigue and creep life. We expect our findings to contribute to the efficient operation of thermal power plants by optimizing the flexible operation factors.