Making Request to new twitch API in java

For the API method you are calling, to put it simply, No authentication is required. Aside from a header containing a Client ID.

You are calling

Which is a GET request not a POST like in your snippet.
This should do what you need:

    url = new URL(("https://api.twitch.tv/kraken/streams?channel="  + channelName));
    connection = (HttpURLConnection)url.openConnection();
    connection.setRequestMethod("GET");
    connection.setRequestProperty("Client-ID",
            YOURCLIENTIDHERE);