I'm looking to incorporate some Kalamata olive brine into olive bread dough to maximize flavor. How much will I have to reduce the other salt in the recipe?
There is no single answer to this. Olives are packed in widely differing brine concentrations, and breads are made with widely different salt concentrations. If you start reading the labels of olives in the supermarket, you will find anything between 1.5 and 7-8% salt.
Luckily, the labels are also your solution here. Just read the label, assume that the olives have reached equilibrium with the brine (this is not too strong an assumption, if you decide to desalt olives at home, you will find that it works within 1-2 days) and calculate from there.
Of course it depends on the saltness of the brine, the volume of brine used, and the amount of salt for the recipe.
This recipe for brining olives uses 3/4 cup of salt for 3 quarts of water. So 1/4 cup per quart, or 12 teaspoons per quart. Since a quart is 192 teaspoons, there are 0.0625 teaspoons of salt per teaspoon of brine.
This recipe for olive bread uses 1/2 teaspoon of salt.
So to replace the salt entirely you would use 8 teaspoons of brine. (This of course neglects the reduction in concentration of the brine due to the olives absorbing some of the salt.)