I don't think there's anything built in to FTP or PHP that will do this directly. You might look into file locking, but I don't know if FTP locks a file as its retrieving or if it parks it in a temporary spot and then moves it to its final destination when its done (I'm thinking its this way).
A possible work around is to have a script create and update a status file. So when the FTPing starts from server 1 to 2, a file is writen to that says something silly like "transfer started" and when the transfer is complete, have another script update that same file with "transfer complete" (or whatever). Rinse and repeat with server 2 and 3 (ideally with a new/different file). These files need to be readable by server 3. Then you can have code on server 3 check these files for the progress of the FTP (and if you were creative, you could check the last modification date of the files to determine when the transfers completed and how recent your file(s) is/are).
