  Gamma-ray flares of blazars may be accompanied by high-energy neutrinos due
to interactions of high-energy cosmic rays in the jet with photons, as
suggested by the detection of the high-energy neutrino IceCube-170922A during a
major gamma-ray flare from blazar TXS 0506+056 at the $\sim3\sigma$
significance level. In this work, we present a statistical study of gamma-ray
emission from blazars to constrain the contribution of gamma-ray flares to
their neutrino output. We construct weekly binned light curves for 145
gamma-ray bright blazars in the {\it Fermi} Large Area Telescope (LAT)
Monitored Source List adding TXS 0506+056. We derive the fraction of time spent
in the flaring state (flare duty cycle) and the fraction of energy released
during each flare from the light curves with a Bayesian blocks algorithm. We
find that blazars with lower flare duty cycles and energy fractions are more
numerous among our sample. We identify a significant difference in flare duty
cycles between blazar sub-classes at a significance level of 5~\%. Then using a
general scaling relation for the neutrino and gamma-ray luminosities, $L_{\nu}
\propto (L_{\gamma})^{\gamma}$ with a weighting exponent of ${\gamma} = 1.0 -
2.0$, normalized to the quiescent gamma-ray or X-ray flux of each blazar, we
evaluate the neutrino energy flux of each gamma-ray flare. The gamma-ray flare
distribution indicates that blazar neutrino emission may be dominated by flares
for $\gamma\gtrsim1.5$. The neutrino energy fluxes for one-week and 10-year
bins are compared with the declination-dependent IceCube sensitivity to
constrain the standard neutrino emission models for gamma-ray flares. Finally,
we present the upper-limit contribution of blazar gamma-ray flares to the
isotropic diffuse neutrino flux.
