I'm pretty sure that you can access the Kindle Owner's Lending Library on the Fire tablets--but make sure and confirm that with someone who owns a fire!
Regarding the Kindle Owner's Library / Unlimited--many of the books in the Unlimited program are available in the KOL, but not all. On Amazon's website, it will show whether books are part of KU, and if they are also a part of KOL, it will also show "Prime-borrow for free". (At least in the US.)
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