Thank you for your post and welcome to the Bose Community.
As far as I am aware, the Google Play Store is not available on an Amazon Fire Tablet and therefore it would not be possible to download the Bose Connect app.
If any members of the community know of otherwise, your input would be greatly appreciated.
I'd just like to make you aware that the Bose Connect app is not critical for the general use of the headphones. You can still connect through the traditional Bluetooth settings on your device.
Please let me know if you have any further questions.
Charlotte G - Community Support
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