It doesn't, no. Flatpaks aren't ideal for CLI software because a lot of what helps with the sandbox mediation doesn't generally apply to CLI applications (e.g, File Open XDG portal only makes sense in a GUI context); and from a package management perspective, while the apps are closely related and built from the same codebase, it'd be advantageous to have them cleanly split to ease maintenance, independant updates, separate dependencies, etc; so if there were a CLI version, I'd imagine it would be under its own name.
The AppImage is likely the best solution for the Joplin CLI app.