You can install the Roku mobile app for iOS or Android to access "The Roku Channel", but that's not the same as accessing the multitude of Roku channels/apps you can access via a Roku device. In general, many Roku channels/apps have a separate app for iOS or Android, so you'd install those to access their content on your phone. Note that if you have a subscription to a premium service that you're paying through Roku you probably won't be able to access it on anything other than a Roku device.
Roku Mobile App - Free for iOS® or Android™ | Roku
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