I suspect you might have a hard time with this in the general case. I don't think an FTP server is required to expose any method of determining disk space or quota information. That sort of thing is really more in the domain of a true shell interface to the server (e.g. telnet), where you can use commands like df.
That said, you can find out what extra, non-required commands are supported for specific FTP servers by establishing a command-line FTP session and issuing the command "quote site help". This should list the available commands, and if you're lucky, you will see "df" among them. If it is, then you can issue "quote site df" to get a reply that contains the disk space information you're after. NI's FTP site actually exposes df and a bunch of other stuff, so you can test things out there.
There are no LabVIEW primitives for doing this programmatically, so it's going to be much more overhead than what you're used to with the PCs on your LAN. I put together a quick example (LV 7.1) that uses the Internet Toolkit VIs to open up an FTP session with an arbitrary server, send a "SITE DF" command, and return the reply string. If you don't have that toolkit, you might consider getting it; otherwise, you could try to develop something similar with the
OpenG Internet Connectivity Tools.
At the end of the day, this still won't be a reliable way to get volume info from an arbitrary FTP server, so maybe other people have some ideas for you.
Regards,
John