The significant increase in the proportion of renewable energy sources (RESs) has elevated risks of extreme ramp events and frequency instability in power systems. In recent years, frequency stability events have occurred in several countries/regions worldwide due to flexibility deficiencies. Generation flexibility has emerged as a critical factor influencing the frequency stability of power systems. This paper proposes a domain of attraction (DOA)-based quantitative method to assess the frequency stability region of power systems with a high proportion of RESs, considering generation flexibility constraints. First, ramp rate is adopted as the core indicator to characterize generation flexibility within automatic generation control (AGC) timescale, through which a nonlinear AGC model with rate saturation constraints is established. Second, the concept of DOA is introduced to define the stability region of the nonlinear AGC. Third, a quadratic Lyapunov-based estimation method is employed to quantitatively analyze the DOA of the nonlinear AGC at different generation flexibility levels. Simulation results demonstrate that increased generation flexibility expands the estimated DOA of the nonlinear AGC, whereas generation flexibility deficiency induces AGC instability. Moreover, state trajectory and time-domain simulation verify that the proposed estimation method accurately represents the stability region of the nonlinear AGC.