I was just struggling with this myself on an old ipad mini (the original) that used to be mine that my husband uses now. I found that if i was logged in under my apple id then I could download an older version of Kindle. Hope this helps!!
Have someone that has successfully "purchased" Kindle any IOS) sign in to your iPAD with their APPLE ID. (or you can purchase using your ID on a newer device) . Have them download the Kindle app (they will have to "purchase" the free app on another device first) . Since they have already "purchased" the app, It will give them the option of downloading an old version. Then have them sign out and you sign in . The kindle app should be there.
How can I get the Kindle app for iOS 9.3.5 on an older iPad mini? Have someone (that could be you) that has successfully installed Kindle (any IOS) on, say, their iPhone iOS10x or higher, then sign in to your iPAD mini with iOS 9.3.5 with their APPLE ID. (or you can install it on their iOS10x device using your ID on a newer device) . Now sign in to your older ipad mini and airdrop the Kindle app. Since the app is already available on the higher OS version, when you attempt to install it on the iOS 9.3.5 (after airdropping) it will NOW give you the option of downloading an old version when it is airdropped to you. Then have them sign out and you sign in . The kindle app should be there. Pay attention to the model of the iPad - not all versions of iPad have an airdrop capability - I think you need iPad 4+. iPad mini 2 is OK as well. To activate airdrop, swipe up from the bottom of the screen. Apple wanted to make it easy to activate/deactivate, that's why it's located there. It will generally not be found in Settings. Make sure that both Wi-Fi and Bluetooth are turned on - the devices use Bluetooth to discover each other and Wi-Fi to download files.
Hey I happen to have the same issue. I accidentally uninstalled the kindle app on my old iPad, the 3rd gen I think now I can't download the app, it says not compatible with this iPad. Did you resolve yours? Thanks
Apple has consistently shown itself to be a greedy, arrogant, expensive, self-serving company. The iPad 2 I purchased brand new in 2011 or 2012 now (2019) won't run Kindle software. That was the specific 1st reason I purchased the iPad. The decision for me to continue to ignore Apple by purchasing equally-capable devices from better manufacturers is very easy for me now. I'll just use the Kindle software on a 2015 tablet PC which I also purchased new. And it does lots more stuff at 75% the cost of the iPad 2. So I don't have to bother myself with Apple again.
Using very old devices to be online can be a huge security risk.
I can still use the Kindle app just fine on an old iPhone 4s that was purchased in 2011. The older versions of the app can still be downloaded and used, if you had downloaded the app originally back when that iDevice was new.
The directions have been posted in this thread several times.
I just successfully installed the Kindle reader on an iPad Mini 1st gen running ios 9.3.5. I signed in using my apple id then opened the App store, selected "Purchased", then selected the Kindle app I had installed on other devices. This prompted me to install an older version that was compatible with ios 9.x. If I just searched for the app, I received a prompt stating I need to upgrade iOS. I was only able to install by going through previous purchases.