I think it's very possible. For instance, Adobe had pursued Adobe Flex 3 on Linux a year ago via Adobe Labs, read more here...

HaXe though, I'm not too sure about. I've only used it for mere moments... it wasn't really for me.

But as it stands, I think that Flash dev on Linux is one of the few things that I'm holding out for. But as it stands, you have the Flex SDK, which is free. There's TextMate, which supports mxml and *.as files. And of course, Flex is Eclipse based, FlashDevelop runs just find under WINE or other virtualization if you're keen to do so.

And don't overlook OpenLazlo. I learned how to code better for Flex 2 via OpenLazlo.