Inability to download a streaming app on Roku which I already own on another device.

Assuming you're in the US, you should be able to add it from this link:

https://channelstore.roku.com/details/ae9a77e6a02e540039dccfcd6fc53706/britbox

However, if you're paying for a subscription through Amazon don't be surprised if that subscription only works on Amazon devices.  Can you sign in on their website?

https://www.britbox.com/us/