Apparently, the best option is to skip tdnf and just use the rpm command.
rpm --install influxdb-0.9.3-1.x86_64.rpm --noscripts
The --noscripts is because the package wants to set up init.d for me, and as we all know, Photon uses systemd. So, along with adding RUN commands for about half of the post-install script, I need to build an influxdb.service file. I see a pull request in my future, once i work all this out.
Building a .service file turned out to be overkill. After briefly growing to a huge mess, my final Dockerfile looks like this:
RUN rpm --install my.rpm --noscripts
RUN ln -s /opt/influxdb/versions/0.9.3/influx /usr/local/bin/.
The "ln" seemed easier than adding the installation directory to my PATH, and lets me run the administrative CLI via docker exec. There's still a couple of tweaks to make, like setting up a VOLUME to hold the database, but this seems to be working well for me.