In Synapse, a listing of remote files can be retrieved with TFTPSend.List(); after calling that method the list is available in property: TFTPSend.FtpList. It's a TFTPList object so you'll have to do some massaging to show the filenames in a listbox.
Indy has similar methods/properties as do most any "framework" FTP client classes, given that LIST is a basic, standard FTP command.
HTH