Maybe simply:
a) transfer files over http protocol (one side of the communication is already done)
or
b) simply transfer files using sockets

You don't need to implement any special protocol to do that. If you only need the actual data (meaning no need for filename, dates, etc.) then just send the data through socket and accept it on the other size. You may want to send the size of the file as the first word of communication to know if you already received the whole transmission.