Does anybody knows good IDE that will allow me to develop flash application on Linux?
There's nothing very stable or advanced out there. Flash development is essentially restricted to Windows at the moment (unless you just want to export movies as SWFs, in which case there are a few options). There is however one promising (open-source) project, Flash4Linux, which is hosted over at SourceForge, though it is still in its Alpha stage.
You may find some useful suggestions over here.
I use Flex Builder for Linux to build applications using Flex. However it can be a bit fiddly to set up currently due to it requiring newer the latest version of the AIR SDK (see the release notes on how to upgrade). Also the MXML editor broken with Eclipse 3.4, so you'll want to stick with 3.3 until they release a patch, or patch 3.4 yourself according to this (untried by me).
In addition to Flex Builder, you can use FDT by PowerFlasher, awesome product.
Website: http://fdt.powerflasher.com
I don't mean to sound a bit mean, but Noldorin's answer is no good at all and misleading, in fact it is fact-less. Flash development restricted to Windows? REALLY?!?!