We demonstrate a flat broadband time-stretched swept source based on extra-cavity spectral shaping. By adjusting the polarization-dependent gain profile and driving current of the booster optical amplifier (BOA), extra-cavity spectral shaping is optimized to generate output with a 1-dB bandwidth of ∼100 nm, 3-dB bandwidth of ∼140 nm and output power of ∼21.4 mW. The short-term and long-term stabilities are characterized. The average cross correlation of 183,485 round trips is 0.9997 with a standard deviation of 2×10-5, indicating high single-shot spectral similarity and high coherence. The noise floor of relative spectral energy jitter is -141.7 dB/Hz, indicating a high short-term spectral energy stability. The proposed highly stable flat broadband time-stretched swept source is applied to an optical coherence tomography (OCT) system. The axial resolution is 10.8 µm. The proposed swept source can serve as excellent light sources in ultra-fast coherent detection systems for high precision sensing and imaging.