I am not sure but Illustrator has some gradient tools that are very unique on the market neither Corel, Xara, Freehand,... do have anything simlar. It´s called meshing technique but I dont know if you used that- becuase that´s certainly not supported by flash either.
I know that freehand converted the gradients in vector stribes with different solid fills. Anyway have you tested the reverse order?- creating a gradient fill in Flash and import it into illustrator- if it works try modifying it a little in illustrator and get it back.

Otherwise I fear that it is incompatible