I need a simple way for multiple running PHP scripts to share data.
Should I create a MySQL DB with a RAM storage engine, and share data via that (can multiple scripts connect to the same DB simultaneously?)
Or would flat files with one piece of data per line be better?
Flat files? Nooooooo...
Use a good DB engine (MySQL, SQLite, etc). Then, for maximum performance, use memcached to cache content.
Keep in mind a couple things: