Motivated by the recently reported evidence of an association between a high-energy neutrino and a $\gamma$-ray flare from the blazar TXS 0506+056, we calculate the expected high-energy neutrino signal from past, individual flares, from twelve blazars, selected in declinations favourable for detection with IceCube. To keep the number of free parameters to a minimum, we mainly focus on BL~Lac objects and assume the synchrotron self-Compton mechanism produces the bulk of the high-energy emission. We consider a broad range of the allowed parameter space for the efficiency of proton acceleration, the proton content of BL Lac jets, and the presence of external photon fields. To model the expected neutrino fluence we use simultaneous multi-wavelength observations. We find that in the absence of external photon fields and with jet proton luminosity normalised to match the observed production rate of ultra-high-energy cosmic rays, individual flaring sources produce a modest neutrino flux in IceCube, $ N^{\mathrm{IC,10 yr}}_{\nu_{\mu},{\mathrm{> 100~TeV}}} \lesssim 10^{-3}$ muon neutrinos with energy exceeding 100~TeV, stacking ten years of flare periods selected in the $>800~$MeV Fermi energy range, from each source. Under optimistic assumptions about the jet proton luminosity and in the presence of external photon fields, we find that the two most powerful sources in our sample, AO\,0235+164, and OJ\,287, would produce, in total, $N^{\mathrm{IC \times 10,10 yr}}_{\nu_{\mu}, \rm all~flares, > 100~TeV} \approx 3$ muon neutrinos during Fermi flaring periods, in future neutrino detectors with total instrumented volume $\sim$ ten times larger than IceCube, or otherwise, constrain the proton luminosity of blazar jets.