If running from the flash player in the authoring tool, you should have a pretty open security surface. A local development configuration means you don’t have to worry about all these things. If you’re still having problems there, it goes beyond these requirements. For that, double check your code, making sure its doing what it needs to do and make sure you have the URL right and all that jazz.
Since it sounds like you’re running flash locally, you’ll need to make sure you publish your SWF with the access network flag (this is what “Local Security Domains” talks about). This is set in the publish settings of the authoring tool under the name “Local Playback Security”. Once thats set, you need to also make sure your crossdomain file is saved on the server you’re trying to load the content from. For example if I’m loading
kirupa.com/data.php the crossdomain file should be on kirupa.com. Then, when you run your SWF, it should be able to load content from a network (thanks to the access network flag) and not be blocked from loading content from the specific site targeted (thanks to the crossdomain file).