open both fla files in flash. open the library in, at least, one of them and click the icon at the top of the library panel that says "new library panel".
use the new library panel's dropdown to select the other fla file's library. now drag from one panel to the other.
p.s. i recommend creating a new folder in the recipient's library so you can drag the movieclip to that folder. (there's often other assets that moved along with the movieclip and it's nice to keep those organized.)
also be careful replaceing on stage items from on fla to another(if its the same name) it will cause a display bug to occur if your useing cs5.
Or, in your source FLA you can temporarily place it on the stage, in its own layer.
Copy the keyframe you just created to hold it.
Open your target FLA.
And, then paste it onto the stage in the target FLA.
The library will update to now include your movieclip and all its parts.
You certainly could do it in a pointlessly complex way, but I wouldn't recommend it. Just right-click in the source library, copy, right-click in the destination library, paste. Done.
Also I'm pretty sure the original poster has figured out how to do this in the five years since this question was originally asked.
Context. Always context. I do most of my work right on the stage.
So, this saves me a few steps.
And, you never know. Poor guy might still be staring at his screen to this day...