Normally when you run an swf file that has to access the internet, you have to upload it to a website and then access it through a browser.
Using the following method, you can run it locally either in a standalone player or in a browser.
Open the following link in your browser http://www.macromedia.com/support/documentation/en/flashplayer/help/settings_manager04a.html and select the Global security settings for content creators link.
Select Edit Locations & Add Location.
Either Browse for Files or Browse for Folders. If you choose the folders option then all swfs in this folder & sub folders will have access to the internet.
Once you have finished adding locations just close the browser window.
If you had flash player running then you will have to re-start it for the settings to take effect. Start the Player and open your swf or open the local html page in your browser.
It should now work as if it is coming from a website.