I didn't have the time to work this out, but maybe try omitting the {0,0} from the second (to the last) BSpline? This shows what I mean for the first and second spline:

Graphics[{EdgeForm[Black], FaceForm[Yellow], 
  FilledCurve[{BSplineCurve[{{0, 0}, {Cos[\[Pi]/7] - Sin[\[Pi]/7], 
       Cos[\[Pi]/7] + Sin[\[Pi]/7]}, {3 Cos[\[Pi]/7] + 
        7 Sin[\[Pi]/7], -7 Cos[\[Pi]/7] + 
        3 Sin[\[Pi]/7]}, {3 Cos[\[Pi]/7] - Sin[\[Pi]/7], 
       Cos[\[Pi]/7] + 3 Sin[\[Pi]/7]}, {0, 0}}], 
    BSplineCurve[{{-Cos[(3 \[Pi])/14] + Sin[(3 \[Pi])/14], 
       Cos[(3 \[Pi])/14] + Sin[(3 \[Pi])/14]}, {7 Cos[(3 \[Pi])/14] + 
        3 Sin[(3 \[Pi])/14], 
       3 Cos[(3 \[Pi])/14] - 
        7 Sin[(3 \[Pi])/14]}, {-Cos[(3 \[Pi])/14] + 
        3 Sin[(3 \[Pi])/14], 
       3 Cos[(3 \[Pi])/14] + Sin[(3 \[Pi])/14]}, {0, 0}}]}]}, 
 ImageSize -> Full]

Interesting approach, Gianluca. Thanks. I had not thought of superimposing two curves for the color & outline. I was hoping to preserve the odd-even filling scheme if possible. Your solution results in a fill of the entire shape.