Microchannels are an important component of the microelectromechanical system （MEMS）， and the rarefaction effects caused by small scale characteristics is an important factor that cannot be ignored in affecting the flow stability of microchannels. Developing stability analysis methods suitable for rarefied flows and revealing the influence of rarefaction effects on the microchannel flow stability are of great significance for function realization and performance improvement of the MEMS. Based on the Boltzmann Bhatnagar-Cross-Krook （Boltzmann BGK） equation and Maxwell boundary condition， parameter influence analysis is conducted on the stability of the plane Couette and Poiseuille flow under low-speed isothermal conditions by solving the eigenvalue problem. In addition， existing research on Rayleigh-Bénard flow focuses on monatomic gases. Using the Navier-Stokes equation combined with modified boundary conditions， the effects of monatomic and diatomic gases on the stability of Rayleigh-Bénard flow are analyzed， considering different molecular models. The results show that for the plane Couette and plane Poiseuille flows， the rarefaction effects and the accommodation coefficient increase both play a stabilizing role. Increasing Mach number exhibits a destabilizing effect on the Poiseuille flow， while the rule of influence on the Couette flow stability is related to the form of disturbance waves （standing or traveling waves）. In the same disturbance patterns， an increasing Mach number has a destabilizing effect， while in different disturbance patterns， the flow becomes more stable with a larger Mach number. For the Rayleigh-Bénard flow， the hard sphere diatomic gas has the largest unstable parameter range compared to the monatomic or diatomic gas in the variable hard sphere and variable soft sphere models. With a large wave number， the rarefaction effects play a stabilizing role， while a greater degree of rarefaction leads to a larger growth rate with a small wave number.