It seems that at least temporarily the 64bit version of Flash Player will not be available for Linux. I found out when upgrading my system, where at some point I got the following error message:

[myPC:/home/leo] update-flashplugin-nonfree --installThe solution is to install the 32bit version of it, as explained here at this forum (another option is to install gnash, but I haven't tried). The details are described on this post, specifically.
ERROR: 64 bit player temporarily not supported
More information might be available at:
http://wiki.debian.org/FlashPlayer