You have two processes here that are discrete,
- Dumping the database.
- Moving the dump to an FTP server.
There are numerous ways to accomplish both of these. You'll have to ask a more specific question about either one.
FTP is an old antiquated transfer protocol that's highly insecure and you should never use it unless you absolutely must. Instead, consider using something like
rsync over SSH. Microsoft has jumped on SSH with the latest version of Windows 10 providing an install option from the Windows Store, and it's likely the most secure method of doing what you're after: if you have control over both the server and the client, I would be using that method for transfer.