Blazars are the most extreme subclass of active galactic nuclei with relativistic jets emerging from a supermassive black hole and forming a small angle with respect to our line of sight. Blazars are also known to be related to flaring activity as they exhibit large flux variations over a wide range of frequency and on multiple timescales, ranging from a few minutes to several months. The detection of a high-energy neutrino from the flaring blazar TXS 0506+056 and the subsequent discovery of a neutrino excess from the same direction have naturally strengthened the hypothesis that blazars are cosmic neutrino sources. While neutrino production during gamma-ray flares has been widely discussed, the neutrino yield of X-ray flares has received less attention. Motivated by a theoretical scenario where high energy neutrinos are produced by energetic protons interacting with their own x-ray synchrotron radiation, we make neutrino predictions over a sample of X-ray blazars. This sample consists of all blazars observed with the X-ray Telescope (XRT) on board Swift more than 50 times from November 2004 to November 2020. The statistical identification of a flaring state is done using the Bayesian Block algorithm to the 1 keV XRT light curves of frequently observed blazars. We categorize flaring states into classes based on their variation from the time-average value of the data points. During each flaring state, we compute the expected muon plus anti-muon neutrino events as well as the total signal for each source using the point-source effective area of Icecube for different operational seasons. We find that the median of the total neutrino number (in logarithm) from flares with duration < 30 d is 0.02 events