When the phrase “I know” is used in English […], it signifies assent and acceptance of the point of view of a conversational partner. It’s a fairly confident assertion of acknowledgement, of agreement.
On the other hand, the questioning “right?” stuck onto the end of a sentence is a request of affirmation of an assertion and a simultaneous invitation to disagreement. Right? Don’t you think so? Do you agree with me?
So when a young speaker (and I’ve only heard this phrase used by speakers under the age of 25) combines the two, it seems to be a simultaneous assertion of confidence and an instant pulling back of that confidence so as not to seem too pushy. It seems to ask for a continuation of the conversation. If the interlocutors continue the conversation, it may branch into areas of disagreement, but so far they are of the same mind.