As near as i can tell from reading the feature chart on their website, this can't be done. It looks like the only destinations they allow are their own viewing software and webpage based viewing. There doesn't seem to be any sort of export-to-video function.
However, if you have a video card with a "video out" function (NTSC or PAL composite), you could connect this output to your VCR and record whatever you see on your computer monitor while viewing the flipbook. There wouldn't be any need for any other software (such as Vegas) at all.
Then again, if you're willing to sacrafice the nifty 3D page turning effects, you could just create your entire project in Vegas to begin with and not bother with Flipalbum at all. Vegas has some nice transition effects such as peel, wipe, zoom, fade, etc that all are very appealing when going from one still to another. With pan & crop you an even add some motion to your stills. Of course, you can also add titles, overlays, picture-in-picture, effects, music, narration, and a few zillion other things too. Then you can output your finished album to tape, CD, video CD, or streaming media files.
I took a quick look at Flipalbum. While cute, I think the page flipping will get tiresome after the first half dozen or so flips. I also noticed the disclaimer on their web site (left inside cover of the "book"). In the demo that you can view from their web site if you install the viewer, they admit they use PDF layering for the images in their ablum. So of course they are showing off their product in its best light, but the montages, special effects, layering, borders, etc.. are done with layers, some looked complex and unless you have and are rather proficient with Photoshop or are willing to purchase that or something like it also, then you're not going to get the same effects they show and in any case not without a climbing a steep learning curve. Interesting that they also say while they made the images in the demo with layering they admit their software does NOT allow editing of PDF. Curious.
Frankly, you are better off with CD burning software like Nero that is feature rich. Really depends what you want to do. If you just want a simple photo album and just static images that can be played in some kind of slideshow then you may want to look at ACDSEE or many other applications. They also support contact sheets, can present as thumbnails, allow zoom etc.. You can also put x number of proofs on a page which is a nice feature for photographers.
If you want to make a video, then Vegas Video or Video Factory if you're on a budget can make some very impressive video slideshows. The advantage is you can add sound tracks, pan, zoom, add titles, overlays and go a little crazy with all the transitions possible.