A novel chalcogenide slot waveguide with asymmetric cores of As \(_2\) Se \(_3\) has been designed to achieve a nearly flat dispersion profile across a broad spectrum ranging from 1.50 to 3.50 µm, with four zero-dispersion wavelengths (ZDW) at 1.64 µm, 2.26 µm, 2.65 µm, and 3.37 µm. An extensive analysis of supercontinuum generation (SCG) has been performed around these ZDWs, including an investigation of its behavior in both normal and anomalous dispersion regimes with a focus on identifying pump wavelengths for maximum broadening and pump wavelengths leading to flat SCG. One wavelength in the normal dispersion regime and one in the anomalous dispersion regime around each ZDW were examined, along with an additional wavelength at the communication wavelength in the normal dispersion regime. The maximum broadening of the supercontinuum generation, spanning 1.624 octaves, has been achieved in the anomalous dispersion regime of the waveguide, pumped by 200 fs pulses centered at 1.55 µm with a peak power of 2 kW. A flat supercontinuum spectrum with a 25 dB spectral flatness, spanning 0.831 octaves from 1.25 to 2.225 µm, has been achieved in the waveguide when pumped at 1.55 µm wavelength with a pulse of duration of 200 fs and peak power of 200 W. Dispersion coefficients up to the tenth order have been included to obtain the converged result for supercontinuum generation.