Unfortunately, Sora resources from UK libraries cannot be transferred to Kindle eReaders or tablets. On a Kindle Fire, you might be able to use the web-based version of Sora rather than the app to access items.
If you have access to a public library in the US, it is possible to transfer items from that library's Sora account to your black & white Kindle reader in the UK.
You can borrow resources from Sora UK and US libraries and transfer them to Nooks and Kobo devices if you install and authorize Adobe Digital Editions (ADE) on your computer and follow the Nook or the Kobo instructions.