I took the .gif file and opened it with Gimp image editor. There are two layers in the image. One is of Sonic, the other is of just the hand in a new position. There is a transparency channel in the one layer of just the hand. It appears that gif2swf has problems with transparency. I've found that as long the background is colored, it will convert ok. So I took the layer with the image of the entire Sonic and duplicated it. I then cut the hand off the duplicated image, and pasted the hand in the second position.
The next issue was to make sure that the background was not transparent or white. For each of the two images, I added a transparency layer and colored to transparent plain white, (color code ff ff ff). I then created two new blank images, and filled with a slightly off white color of fe fe fe. I then pasted each of the two sonics on each of the new backgrounds, and anchored each one.
Finally I took one of the images did a layer, new layer, pasted the second image on and anchored it. That gave me a two layer image. I then exported it as a .gif image, with a delay of 250 ms. Finally I ran gif2swf on the .gif, took the output.swf and renamed it. Attached are the two new files, sonic_two_layer_off_white.gif and sonic_two_layer_off_white.swf.
I know this is not a SWFTools fix to the problem, but it is a work around if people want to use it.