Well, I was messing around with the Flock 1.0 Beta today, and noticed that the automatic install for Flash didn't work -- whether or not this is just a symptom of it being a beta or of some problem with just the Linux client, I don't know. Either way, here's I got Flash working:
1) Download the Flash tarball from Adobe: http://fpdownload.macromedia.com/get/flashplayer/current/install_flash_player_9_linux.tar.gz
2) Unpack it and copy the file "libflashplayer.so" to /home/<your user name>/.flock/plugins/
Maybe there's an easier way, but all I know is that the Flash installer shell script that comes with the download only lets you install it to either Firefox or Netscape (there's no option for Flock).