(Note: only tested in BF4 beta and Chrome on Windows)

Exporting an emblem

1. Log into BF4 Battlelog.
2. Visit the Customize emblem page.
3. Select the emblem you wish to export.
4. Open the console (Ctrl-Shift-J).
5. Enter the following code snippet to copy the raw emblem data to the clipboard:
   copy('emblem.emblem.load('+JSON.stringify(emblem.emblem.data,null,2)+');');
6. Paste somewhere useful, like a gist. Whatever.
7. Close the console (Ctrl-Shift-J).

Importing an emblem

1. Log into BF4 Battlelog.
2. Visit the Customize emblem page.
3. Click the "+ ADD" button.
4. Open the console (Ctrl-Shift-J).
5. Paste the contents of a previously-exported emblem into the console. Make sure you get everything, from the emblem.emblem.load to the ending ;.
6. Click the "SAVE & USE" button in the top right.
7. Close the console (Ctrl-Shift-J).

Enjoy!