I am installing a chair rail that begins parallel to the floor then angles up a staircase. How can I determine the proper angle?

Lay a staright fllat board or mason's level on the stairs so it spans from the front edge of each stair step. The board/ level and be pushed up againist the side of the staircase and the angle measured compared to the wall. It will likely be between 38 degress and 42 degress. This may be of help or interest to you. Stair PanelSet Application Range

As he mentioned above the angles 38 to 42. Id start with a 39 degree at first, now this doesn't mean turn your saw to that degree, you'll need to have that first, which is 19.5 cut that and just see what that looks like then adjust to make it fix better