Since you’re using jQuery, you can easily access the HTML DOM.
Consider an iframe element in your HTML:
<iframe src="" width="1920" height="1110" style="border: none;"></iframe>
You can interact easily with jQuery:
$('iframe').attr('src', 'http://www.twitch.tv/' + stream.channel.name + '/embed');
Information on jQuery selectors: https://api.jquery.com/category/selectors/