This is an unsatisfactory answer, but Fly does run Java/JVM apps via Dockerfiles. The best docs we have for it at the moment are at https://fly.io/docs/getting-started/dockerfile/, but its clearly not written for folks who want to deploy Java apps.

If somebody deploys a Java app to Fly, please consider documenting it at https://github.com/superfly/docs/tree/main/getting-started and we'll merge it into https://fly.io/docs/