The short answer is that you cannot.
Neither of these are capable of amazon connectivity.
The tv is not a "smart" model, and the player is an older (2010) model that did not include amazon support.
These "smart" devices such as the player are extremely limited in capability, they are only able to use the apps that are built into them at the time they are made, and there is no possibility of updating them or adding new features.
Your best option at this point would be to buy a new/separate external streaming device such as a roku or fire tv. Either of these will do everything your bluray apps could do and many more, including amazon prime, and both are much better supported in terms of updates and new features. Samsung no longer supports your player and will never release new updates or features for it.
Best regards, ***** ***** for the news,
I am an independent technician and I've spent my personal time, unpaid, in a good faith effort to assist with the question for which you solicited my services. I am only paid for my efforts when customers such as yourself leave positive feedback for my work. Again I apologize there is not a better outcome here, though this is really beyond either of our control. I do hope you’ll consider leaving a positive rating for me, rather than “shoot the messenger”, so that I may get credit for my time spent in good faith to answer your question accurately.