Yes, LAMS uses Flash for some for some of its interfaces. As Al mentions, the work has done completely from scratch and took a really long while to get it right.
The most difficult part is to get Flash developers, as most of the people that work with Flash are graphic designers but not programmers that can do actual code in actionscript (the scripting language Macromedia uses).
The communication between the Flash movie and the backend is done thru an open XML data transfer standard called WDDX (http://www.openwddx.org/). It's a bit of a nightmare to get your head around it, but in principle, it allows you to serialize Java objects and pass them to Flash, and Flash can make sense of them. However, as you can imagine it ain't so easy, as Flash does not have a rich varieaty of datatypes as Java does, so there's quite a fiddling to do there.
We are currently redoing the entire Flash interface for the next LAMS release (which includes I18N in Flash, resizeable windows, change skins on the fly, etc) and the most difficult part has been the time that it takes you to create a framework in Flash that allows you to do all this. We looked at Lazlo but realized that it wasn't going to be as easy and didn't provide the flexibility we wanted so we went with our home brew recipe.
Now, I've been looking at some of the work the Google fellows have been doing with maps.google.com and it's very very nice. So I guess Javascript is also another option for rich web interfaces.
Surprisingly enough, at times the fact that you require Flash clients on browsers seems to be a bit of a burden for system admins at some Universities or highschools. In addition, Firefox seems to have a memory leak when using Flash for a while (we have experience this at times). Hopefully that will be fix shortly by the Macromedia fellows, but until it gets fix, your application might be suffering a bit, which might be a thing to take into account.
Overall, if you want to go Flash all the way, probably the most difficult part is to get good Flash devs that understand what an object is and are not scared to parse very large and cryptic XML documents 😊
If you want to have a look at the Flash source code in LAMS, you can download the source code from the lamsfoundation.org site.
Hope that helps,
Ernie
