FTP has to be one of the least reliable, most insecure, and most firewall-unfriendly protocols around. I hope the data you're transferring isn't private or business-criticial. If it is and that's all they offer then shame on them.
That said, the problem almost certainly is the firewall. FTP uses port 21 for control and either port 20 or some random port for data, depending on whether you're using passive FTP or not.
Without knowing the app in question, it's hard to tell how to toggle passive FTP. It
may honor the system setting (System Preferences -> Network -> (interface) -> Proxies -> Use Passive FTP), so that would be the first place to look. Otherwise you need to edit your firewall rules to be more permissive in the traffic it will allow to/from their server address (which has other security implications). Generally, if the FTP client doesn't use port 20, it will use any random port number above 1024, but clearly you don't want a blanket firewall rule that allows all traffic (you might as well not use any firewall at all).
If toggling Passive FTP doesn't work, find out from them whether they have any controls for the port numbers to use. Since they've chosen to use FTP they should be prepared to help users with the baggage that comes along with it.