Amazon Prime (Instant Video) app not available for download?

Amazon Instant Video shows any films purchased through Amazon and any Amazon Prime content.

Xbox doesn't have a Prime App, rather Xbox Video which only shows films and shows purchased through Xbox Store.

If films/shows purchased from Amazon aren't showing in Amazon Instant Video app you will need to contact Amazon Customer Support to verify your purchases.

Remember, Amazon Prime content changes so they remove films/shows periodically and add new ones. Amazon Instant Video purchases remain all the time.

Lovefilm is now Amazon Prime Instant Video

Hello Cupid!

Thank you for posting on Xbox Forums! I understand your eagerness to download and watch on the Amazon Instant Video App. However, It appears as though that the app is no longer available to download on the Xbox 360. It would seem that Amazon Prime has
removed the app from the Xbox 360, and the app is only available on the Xbox One. If you have any further questions please feel free to reply back letting us know. Thank you again for posting on Xbox Forums!

Hey GAUV,

I'll post the link again this way:
https://support.xbox.com/en-US/xbox-360/apps/amazon-instant-video-setup

"To watch Amazon Instant Video content on your console, you need:

• To be signed into an Xbox Live
• At least 75 megabytes (MB) of available storage space"

"Install the Amazon Instant Video app

1. From Xbox Home, go to Apps, and then select Browse Apps.
   
2. Browse or search for Amazon.
3. Select Amazon to download the app. Once downloaded, the Amazon Instant Video app automatically starts.
   

To start Amazon Instant Video later, go to Video, My Video Apps, and then select
Amazon."

If you still can't see the app then I would recommend to
clear the console system cache.

It appears that Amazon does have an app for the Xbox 360 according to the FAQs regarding this question.

https://support.xbox.com/en-US/xbox-360/apps/amazon-instant-video-setup

Install the Amazon Instant Video app

1. From Xbox Home, go to Apps, and then select Browse Apps.
2. Browse or search for Amazon.
3. Select Amazon to download the app. Once downloaded, the Amazon Instant Video app automatically starts.

To start Amazon Instant Video later, go to Video, My Video Apps, and then select Amazon.