As per §4.a of the Creative Commons Attribution-ShareAlike license that all Stack Exchange posts are under,
upon notice from any Licensor [Stack Exchange] must, to the extent practicable, remove from the Collection any credit as required by Section 4(c), as requested.
The most obvious way for a contributor to do that is to flag their own post. This is what is mentioned by the Meta.SO post on the subject; I couldn't find any mention in the help center. This transmits the request to moderators, who have no way to honor it and must pass on the request to Stack Exchange staff.
It would be more direct if content disassociation requests went directly to Stack Exchange staff, via the contact form. Please mention content credit removal in the help center — possibly under What is the license for the content I post?