Well I am not entirely sure where the Wikipedia article gets its values, as it is not like anything I have ever seen. Most sources I have seen list slip velocity as being
u_{\mathrm{wall}} \approx \ell \left( \dfrac{\partial u}{\partial n} \right)_{\mathrm{wall}}
where ##u_{\mathrm{wall}}## is the velocity at the wall (slip velocity), ##\ell## is the mean free path, and ##n## is the wall-normal coordinate. This is similar to what your linked Wikipedia article shows except it has a the left side strange. You could certainly rewrite it as
u_{\mathrm{wall}} = \beta \left( \dfrac{\partial u}{\partial n} \right)_{\mathrm{wall}}
where ##\beta## is an unknown proportionality constant that is of the same order of magnitude as ##\ell##. It could also be written as
u_{\mathrm{wall}} = \alpha \ell \left( \dfrac{\partial u}{\partial n} \right)_{\mathrm{wall}}
where ##\alpha## is now the unknown constant whose value is somewhere around (but not necessarily exactly) one. Those form can be derived from the kinetic theory of gases, but the exact value of ##\alpha## or ##\beta## cannot, to my knowledge. The fluids books I have handy don't go through the kinetic theory background of this relation, though apparently it is contained in
https://www.amazon.com/dp/B000859FOO/?tag=pfamazon01-20 if you have access to university library and can find it.
Otherwise, really all it is saying is that the slip velocity is proportional to the mean free path and the shear stress at the wall. The proportionality constant is just chosen such that the best fit with reality is achieved.
