You can install the Kindle App on iPad devices that have iPadOS14 or later installed. Here is direct link to the Kindle App in the Apple App Store:
https://apps.apple.com/gb/app/kindle/id302584613
Once installed and you have signed-in to your Amazon Kindle account, you can download books from your account to your iPad. You should note that older models of iPad that cannot be updated to iPadOS14 or later (i.e., iPad1-4, iPad mini1-3 and iPad Air1) are not compatible with the current version of the Kindle App.
For information, here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:
32-bit devices (obsolete)
iPad1 - iOS 5.1.1
iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi & Cellular)
iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi & Cellular)
64-bit devices
iPad Air1, iPad mini2 and iPad mini3 - iOS 12.5.6
iPad Air2, iPad mini4 - iPadOS 15.7.1
Newer models are all able to be updated to the current version, iPadOS 16.1
- iPad Pro (all models)
- iPad Air (3rd generation and later)
- iPad (5th generation and later)
- iPad mini (5th generation and later)
Not sure which iPad you have? Identify your iPad model.