Your friends should appear on your friend list automatically, as long as you and your friends are connected to your Facebook accounts in the game. You shouldn't need to send invitations with the 'Add Friends' button!
If you can't see your friends despite being connected to your Facebook account, please try following these steps to fix the issue:
- Disconnect the game from your Facebook account
- In Facebook, go to Settings - Apps and then remove Angry Birds Epic
- Sign out of the Facebook app and website
- Connect to Facebook again from the game
Hopefully this helps!