That would be "eu sei o que você sabe". Either in Portuguese or English they have different meanings.
Let me give you the two translations to the letter: "Eu sei que Você sabe" would become: "I know that you know ". "Eu sei O que Você sabe" translates as: "I know THAT THING that you know ". Can you see the difference the article makes?
this o ('o' que) is not an article: it is a pronoun. It means 'aquilo'( = that) So, Eu sei o/aquilo que você sabe = I know what you know)
Is que supposed to sound like qui like it does here? (slow version)
Yes. When the letter E comes at the end of a word it sounds like i /ee/.
Eu sei que você sabe que eu sei que você sabe que eu sei que você sabe que isso é bobagem.
I know what you know! If you share common knowledge with someone else, why isn't this acceptable?
Because it's slightly different. "I know that you know" refers to a topic that has already been discussed. However, "I know what you know" is a more general statement, and the person hearing the statement might have no idea of what you are talking about.