Since I've been found lacking in the trig dept., I've always laid out the control system using my CAD system. I'll outline the steps I go through with the hope that it will be of some help to you in your quest.
I've often thought about setting up a spread sheet on my web site that would do the figuring after a few key inputs were made.
My first step relies on an assumption, I figure that I will have 50 degrees either side of nuetral for my maximum bellcrank throws.
The second step is to determine how much flap throw I want. I often go for 30 degrees up and down, as maximum throws. It's a simple ratio, 50/30 = 1.66666.
If I use a radious of, for simplicities sake, 1 inch for the bellcrank, to attach the flap pushrod to. then the flap horn pushrod attachment will have to be on a radious of 1.666 inches from the center of rotation.
Now that the ratio is established, I have 2 of the needed dimensions, 90 degrees at the atachment point, and the legnth of the short arm or radius legnth, to plug into the Trig so I can determine the angle of tilt.
Since I'm using the CAD system to lay this out. I measure the distancefrom the pushrod attachment point, to the center of rotation for the horn. Trig can be used to come up with the tilt angle.
Now, realistically, the flap pushrod is some distance above the airfoil chord line, so there is a minor discrepancy between what I lay out, and what I come up with using the math. i know I just need to input a couple more points of data to correct it, but the graphic solves so much faster for me.
In any case, I draw a line tangent to the flap horn arc, to the attachment point for the flap pushrod. Another line from the tangent point to the center of rotation of the flap horn. I use the CAD dimensioning routine to measue the angles needed.
I figure you already know this information, but offer it for whatever it's might be useful to your project.