Flash Player 10.1 was Adobe's big update where they focused on providing the GPU decoding support for Windows systems and on the OS X side the support entered beta. At first it looked like the Linux Flash Player might use VDPAU for video decoding, but that never ended up materializing. Instead, Adobe's main Linux engineer just ranted about the Linux video APIs on his blog (he did this twice in fact). This engineer, Mike Melanson, complained about the multiple video acceleration APIs for Linux and how they wouldn't work how he wanted for Flash (though other experts say otherwise).
Adobe should really target VA-API or VDPAU support within the Linux version of their Flash Player, but alas they haven't. VA-API and VDPAU are the predominant video API standards on Linux and are already implemented by many other multimedia applications -- even the open-source Gnash Flash player implemented VA-API support. Targeting VA-API also allows most hardware drivers from the different vendors to also work, thanks to the different libraries created by Splitted Desktop Systems for hooking into VDPAU and XvBA on the back-end.
For those interested in Adobe's Mac OS X video decoding support can read these two blog posts from engineers on the Flash Player engineering team.