Cable-type channels like AMC want to be paid. When you have a paid subscription to a "tv provider" service that carries these channels , they receive their pay out of the subscription fees you pay that provider. When you don't have a subscription to such a provider you are not paying for those channels.
Many cable-type channels, again like AMC, make their content available for streaming on the internet via a "TV Everywhere" channel app for those paying for the channel through a TV provider as mentioned above. That service doesn't have to be a bloated cable or satellite service however. There are several services you can subscribe to and run on a Roku that may carry the channels you are interested in at a lower cost than cable or satellite. Ones that come to mind to check out for any particular channel would include:
• Hulu plus Live TV
• Sling
• philo
• Directv Stream
• YouTube TV
• frndly
• fubu
• vidgo
... there may be others.
There are a number of places on the net where you can look up which streaming providers carry a particular channel of interest. Here are several such pages:
• https://thestreamable.com/channels
• https://www.groundedreason.com/cord-cutting/tv-streaming/how-to-stream-by-channel/
• https://suppose.tv/ (thanks to @DBDukes for this one)
• .. and again, there may be others