How do I download Firefox onto my Amazon Fire 11 Max tablet?

The Amazon Fire tablets are basically Android tablets. Long ago Mozilla did put Android Firefox on the Amazon Appstore however Amazon modified the apk file which the cause problems including with updates and Amazon refused to not do such so Mozilla pulled Firefox off the store.

You can however try to side load the apk file https://archive.mozilla.org/pub/fenix/releases/150.0.3/android/ and the two CPU's it can have is Armv8-A so perhaps try the fenix-150.0.3-android-arm64-v8a apk.

You have probably noticed that Amazon does not ship Firefox in its own store.

There are ways to either get Google Play services first, and then use Play Store like on Android. Or if you'd like to avoid that, research "Aurora Store" for a way how to spoof that process.

Even without the above, you're able to "side load" Android apps — your mileage may vary esp. in terms of keeping the app updated, and getting its data consistently between manual updates, but it's the simplest thing to try. You can follow the steps e.g. in https://support.mozilla.org/questions/1572552 — for best compatibility I'd only probably pick the "universal" bundle from here:

https://archive.mozilla.org/pub/fenix/releases/150.0/android/fenix-150.0-android/