I saw a few topics with questions about deploying Syncthing on Kubernetes, but they had been closed due to inactivity.
This gist has some documentation and manifests showing how I deployed Syncthing on one of my Kubernetes clusters to provide a persistent peer for shares between coworkers. The deployment includes a reverse proxy (nginx) allowing team members to log in to the Syncthing GUI at https://example.com/syncthing/.
Hopefully this example will help someone else with Kubernetes questions.