Imagine a Harry Potter scenario.
is the word order normal here? i expected xem to go before tôi
It's probably easier to spot why the order is correct with the more direct translation "let me see your memory".
"Tôi xem ký ức của bạn" is a noun clause and, as every clause in Vietnamese, the right order is: subject, verb, object.
Does this mean to show how good is your memory?
What does this sentence mean?
To show the person your memory(ies).
I sounds very awkward in English. Does this sentence make sense in Vietnamese?
Yes it sounds like you want to see inside their computer not inside a person's thoughts/feelings/memories. I echo dongsang's question
Another gotcha sentence with an untaught non-vocabulary construction...cho tôi xem. It seems there only to create a sense of frustration and failure, as we'll never likely encounter this expression enough to learn it.
literally translates as "let me see..."
Chỉ có tôi ký ức của bạn
Be right? Chỉ có was earlier introduced as "show"