Unable to use the add_file_member API (HTTP) with C#

Here's an example of one way you might do this:

WebRequest request = WebRequest.Create("https://api.dropboxapi.com/2/sharing/add_folder_member");
request.Method = "POST";
request.Headers.Add("Authorization", "Bearer " + accessToken);
request.ContentType = "application/json";
Stream requestBodyStream = request.GetRequestStream();

JsonSerializerSettings serializerSettings = new JsonSerializerSettings();
serializerSettings.StringEscapeHandling = StringEscapeHandling.EscapeNonAscii;           

var memberSelector = new Dictionary<String, String>() { { ".tag", "email" }, { "email", "email@example.com" } };
var accessLevel = new Dictionary<String, String>() { { ".tag", "editor" } };
var member = new Dictionary<String, Dictionary<String, String>>()  { { "member", memberSelector }, { "access_level", accessLevel } };
var members = new List<Dictionary<String, Dictionary<String, String>>>() { member };
var addFolderMemberArgs = new Dictionary<String, dynamic> { { "shared_folder_id", "248930168" }, { "members", members } };
var addFolderMemberArgsString = JsonConvert.SerializeObject(addFolderMemberArgs, serializerSettings).Replace("\x7F", "\\u007f");
var addFolderMemberArgsBytes = Encoding.ASCII.GetBytes(addFolderMemberArgsString);
requestBodyStream.Write(addFolderMemberArgsBytes, 0, addFolderMemberArgsBytes.Length);

requestBodyStream.Close();

WebResponse response = null;

try
{
    response = request.GetResponse();
}
catch (WebException e)
{
    Console.WriteLine(e.Status);
    Console.WriteLine(e.Message);
    response = e.Response;

} finally {
    Stream responseStream = response.GetResponseStream();
    StreamReader responseReader = new StreamReader(responseStream);
    Console.WriteLine(responseReader.ReadToEnd());

    responseReader.Close();
    response.Close();
}