Escape experiments probed the dynamics of DNA hairpins inside a membrane-embedded α-hemolysin channel, which revealed the orientation and voltage-dependent nature of the DNA-pore interactions. The mean escape times measured at different assisting voltages were strongly influenced by these interactions. Clearly, an escape process from the nanopore was stochastic in nature that occurred in milliseconds. In this paper, we present a new methodology for describing the experimental observations based on the stochastic kinetic approach of discrete-state and continuous-time formulations. Our model considers that a hairpin attains different states inside and out of the pore, and we derived the expression for the escape time distribution from which survival probability of the hairpin that still exists inside the nanopore is determined. On the other hand, the first moment of the above distribution readily yields the mean escape time. Importantly, we show that the recovery of the experimental results was possible taking into account the slow structural fluctuations of the combined DNA-pore system. Additional investigation tested the profound influence of conformational dynamics by considering a pure kinetic scheme, which satisfied the measured data only partially. Therefore, the single stochastic framework suggested here provides a powerful tool that leads to a significant improvement in the theoretical analysis of the experimental results over a range of applied voltages by removing the inadequacy of the original attempt constructed following a number of formulations in the absence of intrinsic fluctuations.