This also means that I have a more difficult path ahead of me, with my Flex Builder trial license already expired.
Fortunately, it's not that hard to setup basic mxml auto complete functionality with a plain Eclipse installation with XML support.
First we need to define the .mxml file association in Eclipse (Preferences > General > Editors > File Associations).

Then map this file association to the XML editor (see screenshot below).

Add the Flex 3 schema (flex3.xsd) to Eclipse's XML catalog.

Try creating a test mxml file and open it from Eclipse.
Test.mxml
[sourcecode language="xml"]
[/sourcecode]
You will most likely receive an Unsupported Type error.

Complete the process by adding the content type definition (shown below).

Close the mxml file and re-open. You should now be able to see the auto-complete functionality in action.

Hope this helps and let me know if you encounter any problems.
If you're a student or a full time Flex developer, you shouldn't even bother trying out the outlined steps.
Flex is free for students. But, if you make a living out of developing Flex apps, you might want to consider buying a license.
Related resources:
