I have built flash sites for a while, and I have used dynamic information for a
while. What I would like to do is build a simple content management system
that would let people login (username and password authentication), then there
would be a new window that would open and they could select which page to
update (from a dropdown box) then type in a field. When they hit save, it
would then write the info from the field as a text file so that the site could
connect to it and use it. Has anyone done this or know how to do it?

You need to use some sort of server; I have done the exact same thing using
coldfusion as my server. You got to set it up so it sends the data to the
server, then the server reads it, and can cerate a txt file.

http://www.macromedia.com/support/flash/applications/creating_forms/

This tutorial shows you how to set up flash to send data. Once the information
is sent, just add an extra tag to create a file. I can only tell you how to do
this using coldfusion. But there are other ways