Apple ID Rescue email

See this support article for help setting up your Rescue email address:

Manage Primary, Rescue, Alternate, and Notification email addresses

Note: If you have forgotten your Apple ID password, then you cannot set up a Rescue email address until you can access your Apple ID profile.

Cheers,

GB

When I click the link to set up a rescue email address, I am brought back to the original link. No solution to my issue of having no rescue email address.

You are doing this on http://appleid.apple.com, clicked the Edit button to the right of the Security section, and answered your security questions ? Have you tried doing it via a different browser ?