Here's a slightly different approach.

[![enter image description here][1]][1]

The solution below treats the three faces as a triangle.
The script calculates all 3 triangle angles, then sums the two smaller angles to find the answer.

As shown in the image below, they are equal to the angle between the edges of the 
larger angle within the triangle.

[![enter image description here][2]][2]

    import bpy, bmesh
    from mathutils import Vector
    from math import degrees, acos
    
    bm = bmesh.from_edit_mesh( bpy.context.object.data )
    centers = [ f.calc_center_median() * bpy.context.object.matrix_world for f in bm.faces if f.select ]
    
    if len( centers ) == 3:
        # Face centers as triangle vertices
        A, B, C = centers
        
        # Triangle edges (sides)
        AB = B - A
        AC = C - A
        BC = C - B
    
        # Triangle angles
        a =       degrees( acos( ( AB.dot( AC ) ) / ( AB.length * AC.length ) ) )
        b = 180 - degrees( acos( ( AB.dot( BC ) ) / ( AB.length * BC.length ) ) )
        c =       degrees( acos( ( BC.dot( AC ) ) / ( BC.length * AC.length ) ) )
        
        # The smallest angle between the two triangle edge vectors equals
        # To the sum of the two smallest angles within the triangle
        angles = sorted( [ a, b, c ] )
        print( angles )
        print( "All: ", sum( angles ) )
        print( "Two smaller: ", sum( angles[:2] ) )
            
    else:
        print( "Invalid number of selected faces" )


  [1]: https://i.sstatic.net/lYj1H.gif
  [2]: https://i.sstatic.net/aAqhf.png