In order to get debugging working with Adobe Flex Builder for Linux Alpha, I had to install the debugger version of the Flash 9 firefox plug-in.
I ran into a strange issue where after installing the Flash 9 debugger plug-in, the next instance of Firefox opened would use this correct flash version, but any other instances of firefox I opened after that would revert back to the regular version of Flash 9.
A quick post to the Ubuntu Forums revealed that running sudo apt-get remove flashplugin-nonfree fixes this without a hitch.