Unfortunately, we haven't found any converter capable of directly exporting flash vector graphics (.fla) to Adobe Illustrator drawings (.ai), except for the Adobe Flash software itself.
It seems that users circumvent the lack of direct converter for the purposes of fla to ai conversion by first exporting the vector to SVG format and then using any of the available svg to ai converters to finish the job.
Alternatively, some users reports to simply use the clipboard, but that requires both Flash and Illustrator installed on same computer.