We perform single-molecule spatial tracking measurements of a DNA repair protein, the C-terminal domain of Ada (C-Ada) from Escherichia coli, moving on DNA extended by flow. The trajectories of single proteins labeled with a fluorophore are constructed. We analyze single-protein dwell times on DNA for different flow rates and conclude that sliding (with essentially no hopping) is the mechanism of C-Ada motion along stretched DNA. We also analyze the trajectory results with a drift-diffusion Langevin equation approach to elucidate the influence of flow on the protein motion; systematic variation of the flow enables one to estimate the microscopic friction. We integrate the step-size probability distribution to obtain a version of the fluctuation theorem that articulates the relation between the entropy production and consumption under the adjustable drag (i.e., bias) from the flow. This expression allows validation of the Langevin equation description of the motion. Comparison of the rate of sliding with recent computer simulations of DNA repair suggests that C-Ada could conduct its repair function while moving at near the one-dimensional diffusion limit.