Flat mode is the way you view messages. Flat mode is where all the messages are on one screen. Threaded is where you view one at a time and click on the title to view the next thread.

To see the difference click "Expand" at the top of the General forum (or any forum) before you click on an individual thread.

All "reading a post in flat mode" means is someone is reading a post and has clicked so that you can't see exactly what post they are reading.

I believe "flat mode" is the default setting to view posts as well. At some point you may also see someone "reading a post in threaded mode". That just requires a lot more clicking.