See if you can get anywhere using the email address of your Roku account and the "forgot password" option when trying to sign in on the AMC+ website. AMC+ does not know your Roku account password, but they may identify you through the email address linked to your Roku account. You may be able to establish a password that you can use along with the email address to sign in anywhere.
In general, if you want to use a subscription on different devices it's best to establish a subscription directly with the provider. Subscriptions through third parties like Roku, Apple, Amazon, etc. often come with significant restrictions.
Roku Community Streaming Expert
Help others find this answer and click "Accept as Solution."
If you appreciate my answer, maybe give me a Kudo.
I am not a Roku employee.