Not sure what fly.io offers vs Heroku or others (I have played with it some time ago but not used for anything serious), but for an equivalent I'd be looking for automated load balancer setup with SSL, easy scaling up so I can go from 1 to 2 or however many web services (with UI or CLI), simple deployment configuration with a Procfile (or whatever) and managed PostgreSQL/MySQL/Redis including backup/restore when needed.

That's more than what I would have or need locally.