Does Cashflow back up automatically?

Yes — Cloud Backup keeps an automatic copy of your data, about once a day, in Cashflow 4.1.0. Turn it on by signing in with Google and enabling automatic backup in Settings → Backup. From then on Cashflow backs up roughly daily when the conditions are right (you’re on a network and there’s data to save), keeps your last 5 backups, and you can tap Back up now any time for an immediate one. Cloud Backup is opt-in and end-to-end encrypted — see Cloud Backup for how it works and how recovery works before you rely on it.

Cloud Backup is an additional copy: your local file and Dropbox backups keep working exactly as before, and keeping at least one of those — especially a Dropbox-stored copy — is still a good idea so a single lost or wiped phone never takes the file with it.