How are you trying to do this?
Use Make Movie Templates Manager or the Custom option to create the flash template.
Custom-Options Button - General tab- User Define Frame Size to 1280 x 720
Frame rate to match your original video file.
Compression Tab - Data rate max 1000kbps
Disable Non - Square Pixel Rendering
Share Create Video File-Custom-or your flash template
Choose the Options button then uncheck Non - Square Pixel Rendering.
If you are using Titles in your project view the Flash file to make sure they are still in position.
If they move, pre render your project to a single video file, then convert to Flash.
Well I'll be dipped in pickle juice. I use VS x4 to make Flash videos all the time and I've tried a few resolutions... but never 1280 x 720. I've tried 720 x 480 and a couple other resolutions that *should* be 16:9, but VideoStudio always screwed up the aspect ratio of the render. However, I just followed your instructions and set it to 1280 x 720, and the render was perfect. (Like the other guys, the aspect ratio selection is set to 4:3 and grayed out so that it can't be changed.)
Geez... I've been trying to get that right for more than a year and just assumed that VS couldn't do it. Thanks for the correct procedure!