Hi… The best way would be to restore the snapshot into a new database app and then pg_dump from in there. (You can use fly sftp get to download the resulting dump file, assuming it’s small—or at least medium-sized.)
The Fly.io platform doesn’t specifically create Postgres dump files themselves. The snapshots are instead at the level of Linux block devices (i.e., the same kind of thing as /dev/hda).
This is normal, actually. You’re supposed to leave that command running for as long as you need the tunnel. (Many people find that surprising.)