I do not think that you can do this automatically very easily. (And if one knows how to do this, I would like to know the answer.)
Multipart is no help, because it structures the content, but not the transmission. Think of it as paragraphs in a text document: They give the text a structure, but it is still one file.
That leads to the real problem: You want to have chunks of a fixed size and send a chunk after one is processed (uploaded to S3), then the next chunk and so on. How does the client know that the first chunk is processed? HTTP does not work the way that you can send new data, when the first one received by the server. You send the next chunk, when the first one is sent (on the way). I'm not sure, whether AFNetworking guarantees to request for the next part, after sending the first part … Maybe it wants to collect small parts.
Why don't you do it, S3 does:
Initiate a upload request with an ID as response. Then send a chunk using that upload ID. If it is done, the server responds and the next part is send. Doing so you have a handshake.