As Iszi noted, a lot of the threats from Adobe products come in the form of privilege escalation and remote code execution vulnerabilities in Flash, rather than features of Flash in general that can be used maliciously. If a malicious Flash script (or PDF, or executable, or anything else) can successfully compromise a machine, any variety of key loggers or network sniffers may be installed.
Additionally, there have been several Flash file overlay vulnerabilities. These problems allow a maliciously designed Flash file to detect keyboard input and mouse clicks without the user's knowledge. The primary purpose of these scripts is for clickjacking, however they could easily work as some sort of a key logger as well. It's important to note that these flaws are browser-based, not backgrounded Flash files.
In terms of defense, certainly removing a ~/.Macromedia directory couldn't hurt, but it might make sense to also
killall npviewer.bin, which will kill all instances of Flash running on your Linux system.
Hope this helped!