I've not personally tried to run a CI installation outside of the standard structure:
Code:
/application/
/system/
/index.php
/.htaccess
Whilst excluding the flexi-auth library from this test, have you been able to get a minimal site example setup with the folder configuration you are trying?
For example - a basic 'Hello World' type page with something more complex like a database request on the same page?
If not, then you need to ensure that CI and its own native libraries are setup with a different folder structure.
If this does then continue to run into trouble, how essential is it that you structure you folders differently?