The "Libby by Overdrive" (Libby) app is not available for download in the Amazon Appstore on Kindle Fire tablets, but the web-based version of Libby will work on most Kindle Fire devices.
On your Fire, open the "Silk" web browser (the icon says, "Internet")
In the address bar, type: https://libbyapp.com/ (or tap the link)
You may wish to bookmark this site for easy access in the future.
Next, follow the step-by-step instructions to set up your account. Note: you will need your library card number. Don't have that information handy? Visit the library at your earliest convenience, and upon presentation of valid photo ID, we can provide you the information. For security reasons, we are unable to give out library card numbers over the phone, email, or chat.
Once you are set up and would like some additional instruction on using Libby's functions, see https://guides.sspl.org/Libby for a step-by-step guide.