It's getting a bit irritating to find that when a goodish bit of industry standard software is released, Linux builds always gets released last or not at all. As an Actionscript developer it was nice to know for a while that Adobe had my back and was actually putting some effort into the development of FlexBuilder for Linux. I've used the IDE for over a year and inspite of its obvious shortfalls compared to the Windows version its been great. Now that's coming to an end since it seems that Adobe feels its no longer worth the time and effort to continue that development program. So once again its time to jump into the wild and see what is out there re, Linux - Actionscript / Flex development.
I've been trialing quite a few and in all honesty none come close to FlexBuilder for Linux (of the ones I have tried). However there are a few promising options out there and my hope is that as more attention comes to bear on these tools theire development teams get all the support they need (financial and otherwise) to make these tools true contenders.
My recommendations for the moment are:

1. IntelliJIDEA: Of all the IDEs out there this seems to be the most complete and competitive. Actually it does seem to have quite a few features  that are an improvement on the FlexBuilder/Eclipse format. It has all the debugging features. It also provides and import from Eclipse feature - though I must comfess I was not very successfull using that feature and got a whole gang of errors - from a project that compiled prefectkly in Eclipse. Installiation is a bit ropey in Ubuntu - and I've found myself constantly having to reset the IDEA_JDK=$JDK_HOME in order to activate the IDE. On occasion I've also found the typing to be a tad slow. However when its settled its a very good IDE. I'm not sure if its because I'm not conversant with it but, its customisation features seem to be quite limited. I'm sure this will improve when the user base expands.

2. AXDT: This is a plug into Eclipse and I found it quite comfortable after installation. Installation though was an absolute pain in the neck. The documentaion is scant and if you try to install unto any version of Eclipse before 3.5 you will really find yourself up against it. I lost 2 Eclipse setups on account of my initial efforts. However on Eclipse Gallileo it installed like a breeze. It is worthwhile to read the installation instructions. Once installed its quite nice and can be somewhat FlexBuilderesque - no doubt because of my familiarity with the Eclipse interface. However it is obviously a work in progress and the first thing you will notice is the lack of a debug feature. In addition it seems impossible to get AXDT to allow you view the compile project in the external browser no matter how many times you set it to do so - though that may be my fault. There's stil a lot of work to be done here but when completed it will be a joy to work with. Its customisation features are none-existent and as I said before, there is virtually no documentation.

3: FDT: Probably better than AXDT - In fact I'm sure it is but its very expensive and so I did not try it

4: Spket: A work in progress no doubt but, may actually turn out to be the best of the lot. Its wierd my saying so because it does not compile Actionscript or MXML at the moment - which I guess should be the core functionality of any Flash building IDE. Its built on Eclipse os its interface is very familiar and it has a lovey drag and drop feature for moving compinents from the library unto the MXML editor - not visual - still it is very nice. However until it can actually run and debug Actionscript it remains just a nice concept