There is an add-on for Kodi to play Amazon Prime videos. This tutorial describes how to install it.
The add-on is not currently compatible with the Raspberry Pi 4 and 5 because the WideVine video module for 64-bit ARM systems does not yet exist.
You must check several points:
Do not have a double authentication enabled on Amazon. Most of the time, login via Kodi does not work because of this extra request.
Enable installation from a zip file in Kodi:
Settings > System > Add-ons.Unknown sources option. Confirm when prompted.Start Kodi.
You should first install a zip file containing the repository information where the Amazon Prime add-on is located. Go to the following address and download the latest Plugin Repository:
https://github.com/Sandmann79/xbmc/releases
Transfer the downloaded zip file to your Recalbox in the desired location in the share.
In Kodi, go to Add-ons > Install from Zip file and select the zip file you downloaded. Confirm the confirmation messages if you have any.
Once installed, still in Add-ons, go to Install from a repository.
Find the add-on in Sandmann79s Repository > Video add-ons > Amazon VOD. Open the add-on to install it. Confirm all necessary dependencies to install it.
Once installed, the add-on should be visible in the list of installed add-ons.
You will need to log in before you can use the add-on.
Open the add-on.
You will automatically have the options window open. On the left, move to Connection on the left and select Sign In....
You will be asked to fill in your email address and password in two windows in a row.
You will probably get windows where you have to retype your password and a captcha. This is quite normal, Amazon does its checks, even if they can be too repetitive.
Once you are logged-in, you will be presented with a window indicating the login process is done.
Now you can enjoy Amazon Prime.