To make this Dockerfile available to all workers in my cluster, I uploaded it to etcd. The path is completely free to choose.
$ etcdctl set /units/tomcat8/Dockerfile < ./Dockerfile
Now I could create a service file for fleet. The instance notation (@) and specifiers (%p, %i) allow to start as many instances as I like, all from one single service file. For details on that review man 5 systemd.service and man 5 systemd.units. I also specified role=worker in the X-Fleet section, to let fleet automatically choose a suitable instance in my cluster.