Total internal reflection fluorescence cross-correlation spectroscopy (TIR-FCCS) has recently [S. Yordanov et al., Optics Express 17, 21149 (2009)] been established as an experimental method to probe hydrodynamic flows near surfaces, on length scales of tens of nanometers. Its main advantage is that fluorescence occurs only for tracer particles close to the surface, thus resulting in high sensitivity. However, the measured correlation functions provide only rather indirect information about the flow parameters of interest, such as the shear rate and the slip length. In the present paper, we show how to combine detailed and fairly realistic theoretical modeling of the phenomena by Brownian dynamics simulations with accurate measurements of the correlation functions, in order to establish a quantitative method to retrieve the flow properties from the experiments. First, Brownian dynamics is used to sample highly accurate correlation functions for a fixed set of model parameters. Second, these parameters are varied systematically by means of an importance-sampling Monte Carlo procedure in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for massively parallel computers, which allows us to do the data analysis within moderate computing times. The method is applied to flow near a hydrophilic surface, where the slip length is observed to be smaller than 10nm, and, within the limitations of the experiments and the model, indistinguishable from zero.