I got these wonderful instructions on updating the Adobe AIR framework for FlexBuilderLinux from Alexis Tejada's blog. They worked for me.

• First of all, backup your sdks/3.x.x folder of your flex builder installation.
• Download the Adobe Air SDK Framework from here.
• Go to the sdks/3.0.0/ folder (in the Flex Builder installation directory).
• Delete the “runtimes” folder.
• Extract the latest Adobe AIR SDK and copy its contents into sdks/3.0.0/, overwriting existing files.
• Go to sdks/3.0.0/bin/ and rename adl and adt as adl_lin and adt_lin (if adl_lin and adt_lin already exist there, remove them).
• Go to sdks/3.0.0/runtimes/air/ and create a symlink “Linux”
  pointing to the “linux” folder in the same directory, go to your
  sdks/3.0.0/runtimes/air/ in the console and type: ln -s linux/ Linux
• Create a new air project
• Project -> Properties -> Build Path -> Library Path -> remove airglobal.swc from under Flex
• Project -> Properties -> Build Path -> Library Path ->
  Add SWC -> add airglobal.swc from previous version (found under
  framework/libs/air in you sdks/3.x.x backup)
• Run

Go and watch the new Star Trek, 'Live long and prosper'!!

Unfortunately there are still problems with this fix and its a hit and miss. We just need to hope Adobe builds the proper support for AIR into the new SDK