  Accurate flux density calibration is essential for precise analysis and
interpretation of observations across different observation modes and
instruments. In this research, we firstly introduce the flux calibration model
incorporated in HIFAST pipeline, designed for processing HI 21-cm spectra.
Furthermore, we investigate different calibration techniques and assess the
dependence of the gain parameter on the time and environmental factors. A
comparison is carried out in various observation modes (e.g. tracking and
scanning modes) to determine the flux density gain ($G$), revealing
insignificant discrepancies in $G$ among different methods. Long-term
monitoring data shows a linear correlation between $G$ and atmospheric
temperature. After subtracting the $G$--Temperature dependence, the dispersion
of $G$ is reduced to $<$3% over a one-year time scale. The stability of the
receiver response of FAST is considered sufficient to facilitate HI
observations that can accommodate a moderate error in flux calibration (e.g.,
$>\sim5\%$) when utilizing a constant $G$ for calibration purposes. Our study
will serve as a useful addition to the results provided by Jiang et al. (2020).
Detailed measurement of $G$ for the 19 beams of FAST, covering the frequency
range 1000 MHz -- 1500 MHz can be found on the HIFAST homepage:
https://hifast.readthedocs.io/fluxgain.
