High-energy neutrinos are expected to be produced during gamma-ray flares of blazars through the interaction of high-energy cosmic rays in the jet with photons. As a matter of fact, a high- energy neutrino event, IC-170922A, was detected at the time of a gamma-ray flare from blazar TXS 0506+056 at the level of 3 sigma significance. In this work, we present a statistical study of blazar gamma-ray flares aiming to constrain their contribution to the blazar neutrino output. We selected 145 gamma-ray bright blazars listed in the Fermi Large Area Telescope (LAT) monitored list and constructed their weekly binned light curves. Using a Bayesian Blocks algorithm to the light curves, we determined the fraction of time spent in the flaring state (flare duty cycle) and the fraction of energy released during each flare. Furthermore, we estimated the neutrino energy flux of each gamma-ray flare by using the general scaling relation $L_{\nu} \propto (L_{\gamma})^{\gamma}$, $\gamma = 1.0 − 2.0$, normalized to the quiescent X-ray or gamma-ray flux of each blazar. Comparison of the estimated neutrino energy flux with the declination-dependent IceCube sensitivity enables us to constrain the standard neutrino emission models of gamma-ray flares. We also provide the upper-limit contribution of flares of gamma-ray bright blazars to the isotropic diffuse neutrino flux.