I was having the same issue. My Epic Games account said that I had successfully linked it to my GitHub account, but I had missed the last step in the process:
You receive an email titled "[GitHub] @EpicTeamAdmin has invited you to join the @EpicGames organization" That email has a green button with the words "Join @EpicGames" on it. Click that and you should finally has access to the GitHub: https://github.com/Oculus-VR/UnrealEngine
The link in the email expires after 7 days, so you might need to unlink/relink Epic Games and GitHub accounts again to get a new email.