Ask user for URL on registration and create feed from the URL on his/her profile page
Since you already know how to do it in PHP, you could use the Panels module. You can then use a Panel to display the user's profile, and you can add a "Custom" field with your php inside.

You could also do something similar by using the Display Suite module and adding a custom code field.

Of course that would require you put php directly into the UI, which isn't always considered the best approach but can be done. To get the user's username, you'd put a field in their profile asking them the user name. That value would then be stored in the $account object.