After contacting the libraries of San Fransico and getting back a very helpful E-mail from the San Francisco Law Library I can now answer it.
- It is likely that a copy of the ordinance text is retained at the San Francisco Law Library in the 1915 SF General Ordinances as a written or taped in addition.
- The Journal of Proceedings of the San Francisco Board of Supervisors, vol 13 (1918) contains the legislative intent as well as the original proposed and accepted "mask law" on page 898 and following. A digitized version is on archive.org, indicating further discussion of the topic later the year. The actual, first issued ordinance is:
Bill No. 5068, Ordinance No. -
(New Series), entitled, "Providing for the wearing of masks or covering over the nose and mouth by certain persons during the prevalence of the epidemic of the so-called 'Spanish flu' and prescribing the penalty for violation thereof."
- The follow-up vol 14 (1919) starts on page 8 with discussing another "mask law" and adjourning that decision. A digital edition also exists on archive.org
Since "The Journal of Proceedings of the San Francisco Board of Supervisors, vol 13 (1918), page 898" is a good citeable source, I ended my inquiry at that position, especially since there are only limited librarians able to look into the physical editions inside the archives and libraries.
Thank you Nate for hinting me to the right archives, I wouldn't have known which library to ask without you.