If you "edit kstest" you'll see some references. The paper by Marsaglia et al. describes how the p-values are computed. The kstest requires that you test against predetermined parameter values.
If I understand the Vose paper by skimming it quickly, the correction described there is intended to deal with the case where you estimate the parameters from the data. In the Statistics Toolbox, the lillietest function is intended for that case. It uses the same test statistic as the Kolmogorov-Smirnov test, but computes the p-value differently. Again, you can edit that function and see the original reference by Lilliefors and some more recent references. It looks like the Vose material and the lillietest function are both based on Monte Carlo simulations, so they may use similar ideas if not identical formulas.