The conductivity of a weekly ionised flowing plasma subjected to weak static electric and magnetic fields has been investigated using the Boltzmann transfer equation (BTE). The velocity dependence of collisions and the effect of flow velocity have been taken into account by using an appropriate collision integral. The dependence of the transport coefficients on Mach number scattering and Hall parameters has been studied in the linear case. The transport coefficients are almost independent of the Mach number in the case of velocity-independent collisions. In a neutral particle collision-dominated plasma the conductivity decreases with increasing Mach number; the converse is however true for an ionic collision-dominated plasma.