So... After some investigation, and if you don't mind using wine + MS Edge, it is possible
1) Install wine-staging
2) Install Edge-dev: https://askubuntu.com/questions/840987/microsoft-edge-on-linux
3) Run Edge:

wine 'C:\Program Files (x86)\Microsoft\Edge Dev\Application\msedge.exe'

4) Log in to amazon prime video and profit

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