.fla files are just Flash Professional files for creating your app. The .swf files that those generate are the ones that actually get loaded in to html and run.
Getting a value from one to the other depends on how you're using them. If they were in separate pages of .html for instance, then you would need to store the values on the users computer via SharedObjects and then retrieve it on the next page. If you're loading a child swf into a parent swf, you can just look up a variable or a property. You'll need to read up on variable scope, specifically how it applies to loaded swfs to understand how that works. It's all just thinking about hierarchy like a staircase and walking up and down the stairs to gain access to different things. Sometimes you walk up one staircase and down another.

FlashDevelop is AWESOME but you might want to just stick with publishing out of Flash Professional until you understand the process a little better.

addChild() is a method provided to any flash entity that is capable of placing a graphical element (display object) on the screen (stage). Sprites (not spirit) are the most bare bones type of these entities. Basically, if it doesn't need frames of animation (timelines), then use a Sprite.