Adobe Flash Player 10.1 abides by the host Browser’s “Private Browsing” mode
Windows, Linux, Mac: Upcoming Adobe Flash Player 10.1, still a beta 2 pre-release, will introduce many new features like the Windows-only H.264 video hardware acceleration support. In this new version flash will accept without objection your wish to browse in the private mode, it will automatically clean-up your flash history once you terminate the session.