I explained how to do the flipping/mirror effect using Virtual Dub awhile back, so this time I will show you how to achieve the same effect using Sony Vegas.
First off you'll want to bring your video into the program and onto the timeline. Next right-click and select "Video Event Pan/Crop" option.
The Pan/Crop window will now be open, which you can do various things (cropping, panning, mirroring). It shows the video in a crop-able box with an F in the center.
Right-click within it and find "Flip Horizontal" this will then cause the F to flip the other direction. You can now click the X in the corner, and you will see in the preview that your video is flipped.
That's pretty much all there is to that, so you can can proceed with whatever else you wish to do afterwards (i.e. rendering)