Never mind found solution.
First use Firefox as your browser (I don't know if there's a suitable plugin in any other one.)
Then install the following plugin:
https://addons.mozilla.org/en-Us/fir...ream-detector/
In the settings for the addon once installed, make sure that when you click on the popup it is set to give you the full FFMPEG command.
Then open another browser, i.e. Google Chrome. Then go to the page on PlayStation Vue for the show you want. Then open the Developer Tools by right-clicking and choosing Inspect Element. Go to the network tab. Then play your desired episode. Search for any link that says something like 4500 m3u8. This will be the HD 720p stream.
Copy the URL and go the following website:
http://osmfhls.kutu.ru/
Paste the URL in and choose whether its a live stream or VOD depending on if you were watching a channel live or a DVR/on-demand recording in Vue.
Finally, click the blue play button.
You should notice a pop-up in the corner from the HLS detector addon. Click on it to copy the URL that is already for ffmpeg and includes the cookie, user agent, and other data for authentication.
Then use ffmpeg in the command prompt and paste the command. It should start downloading without issues.
Maybe this will work for other sites that youtube-dl and streamlink can't handle on their own.