Unfortunately, integrating an existing Flash gallery into a new .fla (authoring file for Flash) isn't the easiest of tasks. While there are ways to do it, I wouldn't classify it as a beginner activity.
I would, though, recommend a number of options:
1. Export your images as .jpegs and created your own simple gallery inside of the Flash web site you are putting together, avoiding the Lightroom Flash gallery all-together.
2. Simple link from the flash web site to the flash gallery. It wouldn't be as seamless as you might like (it wouldn't appear to be all the same thing as it would load a new, slightly different looking page), but it would get the job done.
3. Include your web site flash file in one part of the .html page and the gallery flash file in another part of the page. If you use colors/layout appropriately, it could look rather good. Unfortunately, though, the stock flash galleries out of Lightroom don't make it the easiest to integrate them into a different web page. Other third party flash galleries, like SlideShowPro do a better job at that. I've done something similar here:
http://www.brianreyman.com/portfolio_pages/portfolio_photoGallery.html The gallery (SlideShowPro out of Lightroom) and the menu (custom-built in Flash) are flash and the rest is HTML.