If you are running a 64-bit Linux machine, please note the following advice from Adobe:
"64-bit binaries of AIR are not currently available. Running 32-bit AIR on 64-bit systems has not been fully tested. However, we expect 32-bit AIR to run on these systems if they have the required 32-bit libraries and packages installed. The following instructions describe how to install AIR 1.5 on the 64-bit versions of Ubuntu 7.10, 8.0 and 9.04, Fedora 8 and 10, and openSUSE 11."
If you would still like to install BBC iPlayer Desktop on your 64-bit Linux machine, please follow these instructions at Adobe's website.
For further help you can Contact Us, or you can discuss this issue at the BBC iPlayer messageboard.