So just released on the Adobe Labs website is a new build of Flex Builder 3 for Linux. When I say new build I mean that all the same problems that applied to alpha 4 are there, with the exception of the product’s expiry date, which now gives us over another year to bask in the glory of this dying product.
On the other hand you could try out feiy’s port of Flash Builder 4 Beta 2 to Linux, which I have had some good success with.
Another product people seem fairly pleased with is FDT and according to their site version 3.5 will include better MXML support. As a free plug for them, they support the Red5 project which is now at v0.9.0 RC2 and is a great, free, replacement for Flash Media Server.
All in all you should hope, pray, petition and/or sign FB-19053 (choose whatever suits, but Adobe probably only reads the bug reports…) so that they can give us a working version of Flex/Flash Builder for Linux.