Recently some reports about plugins incompatible with Chromium appeared in the bugzilla, so this is a little explanation what to do in case you hit a problem.
First, Flash works just fine, so you don't have to worry about it. By the way, if you don't like Flash, I recommend this nice FlashBlock extension.
Some plugins are known not to work with Chromium. For example, gecko-mediaplayer may cause you some headaches. If any other plugin is misbehaving, please report it to the Gentoo Bugzilla.
Now you have two choices with plugins. By default Chromium package has USE="plugins-symlink" enabled, which will make it use the system-installed plugins by default, so that things can work out-of-the-box. With more recent versions of the package this USE flag will also prevent installation of known-incompatible plugins. The other choice is to disable "plugins-symlink" USE flag, and manage /usr/lib/chromium-browser/plugins (chromium) or /opt/chromium.org/chrome-linux/plugins (chromium-bin) manually. For the full story see http://bugs.gentoo.org/301911.