Combustion instability identification techniques have received increasing attentions in the design and development of modern propulsion systems, and one of the most popular approaches is the flame transfer function (FTF). This work proposes a novel method to identify the uncertainty quantification (UQ) of FTF. The method is composed of two steps. First, Bayesian approach is applied to model the UQ of impulse function. After the application of prior distributions to impulse function and its variance, the distributions are gradually updated to posterior distributions through incorporation of observed data. Sampling is then drawn from the posterior distributions. For the second step, the uncertainty of impulse function propagates forward to determine the UQ of FTF, through propagation in each sample. This Bayesian approach is then applied to study the combustion dynamics of four liquid-oxygen/kerosene bi-swirl injectors at supercritical conditions. This novel approach is able to capture dominant responses of four injectors, which is characterized by vortex shedding. Not limited to good estimations of impulse functions and FTFs, this method also describes how certain we are of such an estimate. The ranges of uncertainty are small at dominant frequencies and large otherwise, indicating that the dominant responses is unaffected by noise. This method is able to capture dominant responses of four injectors, which is characterized by vortex shedding. This study provides novel perspectives on both transfer function identification and UQ estimation, and will serve as a benchmark for the future analyses of FTF and combustion instability.