What header should be used for sending GZIP compressed JSON from Android Client to Server?

To inform the server that you are sending gzip-encoded data, send the Content-Encoding header, not Accept-Encoding.

This answer shows you that you need to set a header indicating that you are sending data compressed:

HttpUriRequest request = new HttpGet(url);
request.addHeader("Content-Encoding", "gzip");
// ...
httpClient.execute(request);

The answer also shows how to deal with the incoming compressed data.