Diagnosis: the problem probably lies with drawing in Flash, which has a bizarre internal representation of spline objects (by default a shape comprises a stroke -- i.e. spline with border and no fill -- split up into segments, and an interior -- i.e. spline with fill and no border. You can verify this yourself by clicking on parts of a rectangle after drawing it in Flash -- you've just made FIVE objects).
Summary: Flash is just horrible. Don't draw stuff in it.
Solution:
A) Redraw your spline in Illustrator as a single piece.
or
B) Use the hollowed arrow tool in Illustrator to select pairs of vertices in your spline (i.e. where two segments meet) and then command-j or join them together (you'll be asked if you want a corner or tangent, pick the appropriate choice). This will let you sew your bits and bobs into a single spline.