Amazon and Hulu don't hate each other.

Amazon works independently for their prime video and not competitively like Netflix. Hulu exclusives often get the Amazon Original treatment internationally if a TV network doesn't claim the license.

The Hulu app is most certainly on Amazon, otherwise, a fire stick would not have it.

Edit: They hide it if your device isn't "compatible" like if it needs the Widevine version or something.

Fire TV Version and the Android Version probably for Fire Tablets only