Fiber based supercontinuum (SC) sources with output spectra covering the infrared atmospheric window are very useful in long-range atmospheric applications. It is proven that silica fibers can support the generation of broadband SC sources ranging from the visible to the short-wave infrared region. In this paper, we present the generation of an ultrahigh-brightness spectrally-flat 2-2.5 μm SC source in a cladding pumped thulium-doped fiber amplifier (TDFA) numerically and experimentally. The underlying physical mechanisms behind the SC generation process are investigated firstly with a numerical model which includes the fiber gain and loss, the dispersive and nonlinear effects. Simulation results show that abundant soliton pulses are generated in the TDFA, and they are shifted towards the long wavelength side very quickly with the nonlinearity of Raman soliton self-frequency shift (SSFS), and eventually the Raman SSFS process is halted due to the silica fiber's infrared loss. A spectrally-flat 2-2.5 μm SC source could be generated as the result of the spectral superposition of these abundant soliton pulses. These simulation results correspond qualitatively well to the following experimental results. Then, in the experiment, a cladding pumped large-mode-area TDFA is built for pursuing a high-power 2-2.5 μm SC source. By enhancing the pump strength, the output SC spectrum broadens to the long wavelength side gradually. At the highest pump power, the obtained SC source has a maximum average power of 203.4 W with a power conversion efficiency of 38.7%. It has a 3 dB spectral bandwidth of 545 nm ranging from 1990 to 2535 nm, indicating a power spectral density in excess of 370 mW/nm. Meanwhile, the output SC source has a good beam profile. This SC source, to the best of our knowledge, is the brightest spectrally-flat 2-2.5 μm light source ever reported. It will be highly desirable in a lot of long-range atmospheric applications, such as broad-spectrum LIDAR, free space communication and hyper-spectral imaging.