I thought this may be useful for either sending messages or sharing Brawl pictures or movies with each other (seeing how we need to be wii friends to do so). To find your Wii system FC :
1. At the Wii Menu, click on the Wii Message Board in the bottom right corner.
2. Click on the "Create Message" option.
3. Choose the "Adress Book" on the far right. You will be met with your own Wii system FC.
My FC is the first one in my signature.