  Tsinghua University-Ma Huateng Telescopes for Survey (TMTS) aims to detect
fast-evolving transients in the Universe, which has led to the discovery of
thousands of short-period variables and eclipsing binaries since 2020. In this
paper, we present the observed properties of 125 flare stars identified by the
TMTS within the first two years, with an attempt to constrain their eruption
physics. As expected, most of these flares were recorded in late-type red stars
with $G_{\rm BP}-G_{\rm RP}$ > 2.0 mag, however, the flares associated with
bluer stars tend to be on average more energetic and have broader profiles. The
peak flux (F_peak) of the flare is found to depend strongly on the equivalent
duration (ED) of the energy release, i.e., $F_{{\rm peak}} \propto {\rm
ED}^{0.72\pm0.04}$, which is consistent with results derived from the Kepler
and Evryscope samples. This relation is likely related to the magnetic loop
emission, while -- for the more popular non-thermal electron heating model -- a
specific time evolution may be required to generate this relation. We notice
that flares produced by hotter stars have a flatter $F_{{\rm peak}} \propto
{\rm ED}$ relation compared to that from cooler stars. This is related to the
statistical discrepancy in light-curve shape of flare events with different
colors. In spectra from LAMOST, we find that flare stars have apparently
stronger H alpha emission than inactive stars, especially at the low
temperature end, suggesting that chromospheric activity plays an important role
in producing flares. On the other hand, the subclass having frequent flares are
found to show H alpha emission of similar strength in their spectra to that
recorded with only a single flare but similar effective temperature, implying
that the chromospheric activity may not be the only trigger for eruptions.
