The Green-Kubo formalism for evaluating transport coefficients by molecular dynamics has been applied to flexible, multicenter models of linear and branched alkanes in the gas phase and in the liquid phase from ambient conditions to close to the triple point. The effects of integration time step, potential cutoff and system size have been studied and shown to be small compared to the computational precision except for diffusion in gaseous n-butane. The RATTLE algorithm is shown to give accurate transport coefficients for time steps up to a limit of 8 fs. The different relaxation mechanisms in the fluids have been studied and it is shown that the longest relaxation time of the system governs the statistical precision of the results. By measuring the longest relaxation time of a system one can obtain a reliable error estimate from a single trajectory. The accuracy of the Green-Kubo method is shown to be as good as the precision for all states and models used in this study even when the system relaxation time becomes very long. The efficiency of the method is shown to be comparable to nonequilibrium methods. The transport coefficients for two recently proposed potential models are presented, showing deviations from experiment of 0%-66%.