In this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (CNT) system have been investigated. The Visco-Pasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. Both of the CNTs convey a viscose fluid and a uniform longitudinal magnetic field is applied to them. The fluid velocity is modified by small-size effects on the bulk viscosity and the slip boundary conditions of nano flow through the Knudsen number (Kn). Using von Kármán geometric nonlinearity, Hamilton’s principle and considering longitudinal magnetic field, the nonlinear higher order governing equations for Reddy beam (RB) theory are derived. The differential quadrature method (DQM) is used to obtain the nonlinear frequency and critical fluid velocity (CFV) of the fluid conveying a coupled system. A detailed parametric study is conducted, focusing on the effects of parameters such as magnetic field strength, Knudsen number, aspect ratio, small scale and elastic foundation on the in-phase and out-of-phase vibration of the nanotube. The results indicate that the natural frequency and the critical fluid velocity of double bonded Reddy beams increase with an increase in the longitudinal magnetic field and elastic medium module. Furthermore, the results of this study can be useful for designing and manufacturing micro/nano- double-mechanical systems in advanced mechanics applications by controlling nonlinear frequency with an applied magnetic field.