@The_Mike_P-
The Roku Channel can be viewed via the official Roku Remote app for iOS and Android. On the Android version (don't know how similar the iOS interface is), if not on the initial screen, click the X in upper left to return to initial screen. Scroll way down to the "The Roku Channel" section. When you click on a show to watch you will be given an option "Watch now on mobile".
You can also go to TheRokuChannel.com via a web browser on a computer or mobile device.
I don't have any premium channels through Roku to check, but using these two methods you may only have access to actual The Roku Channel content, not premium subscriptions you normally view through The Roku Channel on a Roku TV or device.
Roku Community Streaming Expert
I am not a Roku employee, only a user like you. Please, no support questions via private message -- post them publicly to the Community where others may benefit as well.
If this post solves your problem please help others find this answer by clicking "Accept as Solution.".
Ultra 4800 | Streaming Stick 4K+ 3821 | TCL Roku TV 43S245/C107X