This may be an old thread but I came across it and figured that I would give a final answer.
The twitch api is json based and to recieve your stream key you need to authorize your app for use with the api. You do so under the connections tab within your profile on twitch.tv itself.. Down the bottom of said tab there is "register your app" or something similar. Register it and you'll get a client-id header for your get requests.
Now you need to attach your Oauthv2 key to your headers or as a param during the query to the following get request.
curl -H 'Accept: application/vnd.twitchtv.v3+json' -H 'Authorization: OAuth ' \ -X GET https://api.twitch.tv/kraken/channel
As you can see in the documentation above, if you've done these two things, your stream key will be made available to you.
As I said - Sorry for the bump but some people do find it hard to read the twitch* api.
Hope that helps somebody in the future.