Via Adobe Labs there's the release now of "Square", which is their codename for this next Flash development milestone that brings native x86_64 support to 64-bit Windows/Mac/Linux operating systems with 64-bit web-browsers.
The only other main feature brought by this Flash Square milestone right now is with the Windows version adding hardware acceleration support within Microsoft Internet Explorer 9, which recently was released to the public as beta. The Linux version of Adobe's Flash Player meanwhile continues to go without any form of video hardware acceleration. Adobe's lead Linux engineer has ranted about Linux video APIs but in the end there still is no support and if there is ever support you will likely see it come via VA-API and/or VDPAU interfaces.
Those interested in downloading this new Adobe Flash beta for x86/x86_64 Linux can find it at Adobe Labs. There is also Gnash and Lightspark as free software Flash/SWF alternatives, both of which support 64-bit Linux and the former even supporting VA-API for video acceleration on capable drivers/hardware.