Unfortunately the Piobert-Vieille's law
$$r_b = aP^n $$
is strongly empirical. In order to get the right values for the tuning coefficients what you need to do is experiments. For example sample burning experiments in which you craft a small sample of propellant, you ignite it and then you record (for example with a high-freq camera, but there are other methods...) the flame propagation speed. Knowing the material properties and repeating the experiment at different conditions, you can plot burning rate charts that then you can fit to obtain the values for the coefficient.
For what concerns practical suggestions, for $KNO_3 + \textrm{sugar}$ propellants you can check out the Nakka's Website. In particular in the software section of his page you can find an Excel spreadsheet where you can somehow design your SRM (Solid Rocket Motor) on the base of his own experimental burning rate data.
In my experience when working in my university rocket team, sugar-based formulations are very, very, dependent on the environment in which you prepare the grains. In particular the degree of humidity was highly influencing our combustion chamber pressure and, hence, burning rate and thrust.