You cannot use a standard GET request. You must obtain the access_token and then POST the necessary parameters.
The steps are currently:
Register your app.
Link it with a post here on Stack Apps that has a legitimate [app] or [script] tag. In most cases you will also tag it with placeholder.
In your app:
Have the user authorize your app and ...
First can I say, you might want to use your own icon. Font Awesome is a very useful and easy to use icon toolkit that lets you add icons with simple CSS classes. You could use http://fontawesome.io/icon/star/ if you want :)
Don't use the default button. That's bad UI anyway.
Add your own favorite button for each answer.
And, since you will be using your own classes, like:
<a class="myStarOff" href="#" data-ansID="1234" title="Click to add as favorite answer (click again to undo)">
<a class="myStarOn" href="#" data-ansID="56789" title="Click to ...