The dynamic and transport properties of swarms of ions in a uniform electrostatic field are studied by using a molecular dynamics method. For a representative system, K+ in Ar, using a universal interaction model potential, second and third order ion-velocity correlation functions are determined at various field strengths. From them, Fickian diffusion coefficients parallel and perpendicular to the field, as well as higher order diffusion coefficients, Q(zzz), are obtained within estimated overall accuracy 5% and 7%, respectively. Comparisons of the Fickian diffusion coefficients against results of the moment solution of Boltzmann kinetic equation and a Monte Carlo simulation method using the same interaction potential as well as against experimental data, reveal consistency among all calculation procedures and in addition agreement with drift tube measurements. These comparisons provide new tests for the accuracy of the employed interaction potential. The method has been applied for up to third order velocity correlations and diffusion coefficients but it is extendible to higher order dynamic and transport properties.