Older versions of BB FlashBack did offer export to FLV/SWF flash formats, among the other default video options , but the latest version of FlashBack Pro / Express no longer feature the support for Flash content.
If you still need it, you have to use any of the existing export options to make it with the help of another software, or find old version of BB FlashBack somewhere. But direct fbr to flv conversion is currently not possible.
Updated: October 26, 2023