I have a Samsung UN46EH5300 and it does great with the Amazon app. Always update to the latest firmware.
However, their Blu-Ray players are another story. They do not have the Amazon app. Here' a transcript from a chat with them two days ago:
Powell: Hi, thanks for reaching out to Samsung tech support. How can I help you today?
Visitor: A quck question:
Powell: Please go ahead.
Visitor: I have a Samsung Smart TV and it does great streaming Amazon Instant Video. But, I have older TV's in the house and want to make them "smart". Will Blu-Ray players like the BD-E5900 or BD-E6500 stream Amazon Instant Video?
Powell: I understand that you want to know if you connect Blu-ray player BD-E5900 or BD-E6500 to TV, if you can access Amazon app or not.
Powell: I apologize for the inconvenience caused to you.
Powell: I'm sorry to inform you that Amazon app is not yet available for Blu-ray players. You can connect the player to TV and access other apps on the player.
Visitor: Do you know if the app will be added or if it will be included on the upcoming 7500?
Powell: I'm sorry, we don't have any information about it.
Visitor: Thank you.
I'd love to use their Blu-Ray player so I have a similar interface in both rooms but right now cannot.
You can get a list of all Amazon Instant Video compatible devices on the Amazon web site.