The influence of gas flow rate on breakdown properties and stability of pulsed dielectric barrier discharges (DBDs) in a single filament arrangement using a gas mixture of 0.1 vol. % O2 in N2 at atmospheric pressure was investigated by means of electrical and optical diagnostics, accompanied by fluid dynamics and electrostatics simulations. A higher flow rate perpendicular to the electrode symmetry axis resulted in an increased breakdown voltage and DBD current maximum, a higher discharge inception jitter, and a larger emission diameter of the discharge channel. In addition, a shift of the filament position for low gas flow rates with respect to the electrode symmetry axis was observed. These effects can be explained by the change of the residence time of charge carriers in the discharge region—i.e., the volume pre-ionization—for changed flow conditions due to the convective transport of particles out of the center of the gap.