Abstract Blazar flares have been suggested as ideal candidates for enhanced neutrino production. While the neutrino signal of γ-ray flares has been widely discussed, the neutrino yield of X-ray flares has received less attention. Here, we compute the predicted neutrino signal from X-ray flares detected in 66 blazars observed more than 50 times with the X-ray Telescope (XRT) on board the Neil Gehrels Swift Observatory. We consider a scenario where X-ray flares are powered by synchrotron radiation of relativistic protons, and neutrinos are produced through photomeson interactions between protons with their own synchrotron X-ray photons. Using the 1 keV X-ray light curves for flare identification, the 0.5-10 keV fluence of each flare as a proxy for the all-flavour neutrino fluence, and the IceCube point-source effective area for different detector configurations, we calculate the number of muon and antimuon neutrinos above 100 TeV expected for IceCube from each flaring source. The bulk of the neutrino events from the sample originates from flares with durations ∼1 − 10 d. Accounting for the X-ray flare duty cycle of the sources in the sample, which ranges between ∼2 and 24 per cent, we compute an average yearly neutrino rate for each source. The median of the distribution (in logarithm) is ∼0.03 yr−1, with Mkn 421 having the highest predicted rate 1.2 ± 0.3 yr−1, followed by 3C 273 (0.33 ± 0.03 yr−1) and PG 1553+113 (0.25 ± 0.02 yr−1). Next-generation neutrino detectors together with regular X-ray monitoring of blazars could constrain the duty cycle of hadronic X-ray flares.