Now presenting the alpha of the Flex Builder IDE on Linux! (this was announced at the Adobe MAX 2007 conference). You can now create Flex projects, write code with intellisense-like hinting, compile and debug all within an IDE based on Eclipse, on Linux. You heard it right, it's officially supported by Adobe. Download it NOW.
The future direction of Flex Builder on Linux depends mostly on community feedback. Yes, seriously. So please do write in your feedback even if it is just "works well" or "it sucks". Why is this important? The more the feedback, the more thought will be given to the product. This is how things work in Adobe (as far as I've seen). So again, voice your opinion on what you think of Flex Builder on Linux, and what you'd like to see and not see in it.
Disclosure: I am part of this project. I mostly handled the Linuxisms in the IDE functionality.