The first step of this work is the determination of the elastic and inelastic ion-molecule collision cross sections for the main ions (N2+, O2+, CO2+, H2O+ and O−) usually present either in the air or flue gas discharges. The obtained cross section sets, given for ion kinetic energies not exceeding 100 eV, correspond to the interactions of each ion with its parent molecule (symmetric case) or nonparent molecule (asymmetric case). Then by using these different cross section sets, it is possible to obtain the ion swarm data for the different gas mixtures involving N2, CO2, H2O and O2 molecules whatever their relative proportions. These ion swarm data are obtained from an optimized Monte Carlo method well adapted for the ion transport in gas mixtures. This also allows us to clearly show that the classical linear approximations usually applied for the ion swarm data in mixtures such as Blanc’s law are far to be valid. Then, the ion swarm data are given in three cases of gas mixtures: a dry air (80% N2, 20% O2), a ternary gas mixture (82% N2, 12% CO2, 6% O2) and a typical flue gas (76% N2, 12% CO2, 6% O2, 6% H2O). From these reliable ion swarm data, electrical discharge modeling for a wire to plane electrode configuration has been carried out in these three mixtures at the atmospheric pressure for different applied voltages. Under the same discharge conditions, large discrepancies in the streamer formation and propagation have been observed in these three mixture cases. They are due to the deviations existing not only between the different effective electron-molecule ionization rates but also between the ion transport properties mainly because of the presence of a highly polar molecule such as H2O. This emphasizes the necessity to properly consider the ion transport in the discharge modeling.