To be honest it wasn't that hard to figure this one out, although in your create a class it shows that your gun has damage on, i am not entirely sure if this takes affect in the game, someone please mind testing that out. Anyways enough about that lets get on with tutorial.
What you need:
Call of duty elite, free version you don't have to be premium just sign up and link your account
A shotgun with damage on it!
Here is how to do it:
Step 1. On your console, make a class with a shotgun and choose damage as the proficiency.
Step 2. On console back out to the main menu and on your laptop/pc Head over to call of duty elite.
Step 3. In call of duty elite click on the class that you have just setup (the shotgun with damage).
Step 4. Choose the weapon that you want to have damage on and put the kick proficiency on it.
Step 5. Send changes to game.
Step 6. On console go to multiplayer from the game menu.
Step 7. Go to your vault so it can fetch your profile.
Step 8. Once you are in your vault quickly head into online, create a class, and go the the class that has your shotgun on and click on your shotgun and wait at the proficiency selection screen.
Step 9. A message should pop up saying would you like to integrate the changes you have made on call of duty elite, click yes.
Step 10. Now you should be back at the proficiency selection screen, select damage and your done!
Someone please mind confirming that this actually has affect in game, I did not have time to.
Sorry for my bad english and i hope this works for you as it has worked for me and a couple of my friends without failure.