You go to GOG.com in your browser (using Galaxy Client won't work), then go to your account/library. On the game click downloads/extras, then click Serial Key. Then, on the Paradox Account section use that key under "Redeem Codes".
I know because I just did it all. It took over an hour (or more) for the avatars and icons to appear for me.
Thanks, been looking in the client, never though to take a look on the website for it.