If you are the publisher of a zine and want to digitally preserve your zine on AO3, see the AO3 Fanzine Scan Hosting Project and contact Open Doors.
To preserve physical items, Open Doors partners with several institutions as part of the Fan Culture Preservation Project (FCPP). This project is dedicated to preserving fannish artifacts such as letterzines, fanzines, and other non-digital fan works and memorabilia. Please check out the FCPP website, the FCPP FAQ on this webpage, or contact the Open Doors Committee for more information.