Spur Gear Contact Stress and Strength

Best thing to do is to read a bit more on gear design and analysis.

Load distribution factors are calclated based on experience or are measured. For design purposes, there are a lot of calculation techniques available that can give a rough indication, but load distribution is highly dependant on gear design, bearing stiffness, shaft stiffness and design and housing so you need to verify which parameter is taken into account for a given calculation method.

Calculating the load distribution based on these factors in design phase is complex and can be done using software like KISSsoft, Romax and the like. All of those have one thing in common: FEM. So if you have a decent CAD-system available that can model tooth flank and root (that's the killer), you can model and calculate yourself.

Analytically, best thing to do is to start out with a value you feel comfortable with (f.i. kHbeta = 1.3) and start from there your your design and rating calculations.