The easiest way would be like that pseudocode
while( isFileTransferToServerPending() )
{
SendNextFileToServer();
}
It is also the normal solution because file transfer will be the bottleneck, so multiple file transfer wont speed up your solution.
You can think about complex scenarios, as implementing some client/server logic in which you get a identifier from the server which is identifying the file and the client is packing multiple file data with that identifier and packet stamp to send it to the server.