Making a transparaent background of flash video file is not impossible. It's the same way as making othertransparent background of video file. You just need a contrast solid color for background movie then using alphasetting to make it hole.

Step 1

Install and Run Flash Video Studio from here

Step 2

Click on Browse button under Select tab menu to select your video file

Step 3

Select bounching_ball.avi

Step 4

Go to Settings tab menu (Step 4) and choose Flash 8 + Alpha as video format

Step 5

Go to Effect tab menu (Step 2) and click on "Set alpha channel" button.
Under Alpha Settings window, move your cursor to preview area. Note, your cursor changes to a pick shape, and is ready topick the area where a solid distinct background reside. Click the red area.
You can leave the Check sign on at "Show transparent area as checkeredboard pattern" checkbox to see the transparent area.

Click on the OK button to exit and save from the window

Step 6

Go to Publsih tab menu. Select FLV file as the output format and your video file is ready to convert to a transparentflash video

Step 7

Congartulation!, your have made the transparent flash video file.

Here is the result: