You'll need a router that lets you port-forward FTP requests to the FTP server. Most SOHO routers will do that. I don't know what FlashFXP is, but it looks like it's only an FTP client. You'll need an FTP server. There are plenty of those to be had. At any rate, once you have your FTP server set up and listening, configure your router to forward FTP requests and data (ports 21 and 20) to your FTP server.
As for seeing the drives from the machines inside your home LAN, if the FTP server is a Windows machine, why not just publish the drives on the network using windows file sharing? If it's a Linux machine, you can install and use Samba to do the same thing. Then you just use My Network Places to browse to the FTP machine from the other machines on your home LAN. (I'll assume you already have the home LAN set up.) If you want to make those network drives more "permanently" available, look into mapping the FTP server's drives as a network drive on your computer. You'ld definitely want to leave the FTP server on full time if you do that or the boot time for your own computer can become very long.
