The example you point to is not done in Flash. If you want to do the same type of design as the example you point to then try right clicking the web paage and choose View Source. Since the image slideshow appears to be done use some jQuery approach, you might be able to determine some information from the page code. You could try posting in the Dreamweaver forum if you want to see if anyone can provide some guidance for an approach.
This could be done using Flash. If you want to find some info for how to do it you can search Google using search terms like "AS3 slideshow tutorial"
One of my favorite full featured Flash galleries is SlideShowPro. It comes with an amazing back end, elegant design and best practices coding. You can try it and if you like it the price is dirt cheap ($39) compared to sitting for hours trying to code your own. Time is money..
I would highly recommend getting Director as well. That makes something that sounds tedious like adding all your photos actually fun.