You do not seem to be showing as a Subscriber to the channel. The Discord server is subscriber only at the moment.
There is a Subscribe
button in the top right of this page.
If you have subscribed make sure that everything is properly linked to your account.
The instructions for joining the server are here
It can take up to an hour for the Twitch and Discord servers to link, if it doesn't show up you should try later.
Hope that helps.