Ab initio molecular dynamics simulations are used to describe the connection between dynamic and structural properties in liquid Al90Ni10 and Al80Ni20 alloys at various temperatures. We find that self-diffusion coefficients and viscosity are strongly composition-dependent while their temperature dependence follows an Arrhenius-type behavior, in close agreement with experiment. Through comparisons between both alloys and the corresponding pure elements, we demonstrate that the composition and temperature dependence of these transport properties can be related to the detailed description of the short-range order and more particularly to the interplay between icosahedral short-range order and chemical short-range order. Finally, all our results are used to discuss the known correlation between transport properties and the two-body excess entropy.