Login to PrimeVideo using .Net Core C#

I need to scrape some html from the [login to view URL] website. To do this, I need to first login using a HttpClient, so I can do http requests as a logged user. PrimeVideo website redirects to [login to view URL] for login then back to primevideo, so it's a bit complex than simply post form data and get the cookie. I need the code to login then make a http call to get the html for an internal webpage. No parsing of resulted html is needed, retry or exception handling. Just a working code to start with. Code should be used on Linux, too, so try to avoid any Windows-specific dll or .exe files. Please note that I cannot provide login/password because they're linked to the Amazon account and credit card, so if you're not a Prime member you need to use the 30 days trial.