Gamma-ray flares from blazars have been suggested as ideal periods for the detection of high- energy neutrinos. In fact, the first ∼3σ high-energy neutrino source association was based on the detection of a single neutrino (IC-170922A) coincident with the flaring blazar TXS 0506+056. To better understand the contribution of gamma-ray flares to the blazar neutrino output, a statistical study of the flare properties is needed. Using public data from the Fermi Monitored Source List for 142 bright blazars, we construct a sample with the fraction of time spent in the flaring state (i.e. the flare duty factor) and the fraction of energy released during its flare. We predict the neutrino output of each source during gamma-ray flares using a theoretically motivated relation between neutrino and gamma-ray luminosities (i.e. the neutrino luminosity is proportional to the gamma-ray luminosity to the power of 1.5 − 2.0). We use the quiescent X-ray flux of blazars, as determined from public Swift-XRT data, to estimate the neutrino flux during non-flaring states. By comparing our results with the IceCube sensitivity for week-long transients, we constrain the standard leptonic scenario for the blazar gamma-ray emission, and provide the upper-limit contribution of gamma-ray flares of bright blazars to the isotropic neutrino background.