  Fast radio bursts (FRBs) are bright radio transients of micro-to-millisecond
duration and unknown extragalactic origin. Central to the mystery of FRBs are
their extremely high characteristic energies, which surpass the typical
energies of other radio transients of similar duration, like Galactic pulsar
and magnetar bursts, by orders of magnitude. Calibration of FRB-detecting
telescopes for burst flux and fluence determination is crucial for FRB science,
as these measurements enable studies of the FRB energy and brightness
distribution in comparison to progenitor theories. The Canadian Hydrogen
Intensity Mapping Experiment (CHIME) is a radio interferometer of cylindrical
design. This design leads to a high FRB detection rate but also leads to
challenges for CHIME/FRB flux calibration. This paper presents a comprehensive
review of these challenges, as well as the automated flux calibration software
pipeline that was developed to calibrate bursts detected in the first CHIME/FRB
catalog, consisting of 536 events detected between July 25th, 2018 and July
1st, 2019. We emphasize that, due to limitations in the localization of
CHIME/FRB bursts, flux and fluence measurements produced by this pipeline are
best interpreted as lower limits, with uncertainties on the limiting value.
