This is not a phrase I've really come across in British or Australian English so potentially more of an American English phrase. The phrase comes from sport potentially, with the idea of passing or kicking a ball to someone who then becomes the focus of attention. Therefore, instead of 'let's kick it back on over to' you could instead say 'let's pass it on to...' or some broadcasters say 'and now over to...'. The phrase makes sense without 'on over' so it could just be emphasis or how this particular person uses this phrase most naturally.

Let’s kick it back on over to John. Let’s pass it over to John. Let’s pass it back to John. Let’s pass it back on over to John. Let’s pass it on to John. Let’s pass it on over to John. Let’s toss it back to John. Let’s throw it back to John. Let’s throw it over to John Let’s turn it over to John. Etc. They are all easily understood and vaguely derived from sports. They aren’t regular expressions with clear derivations from a specific sport. They’re just stylistic variations of “I’m done. The next speaker is”

Thank you, Bill! It does sound sport-related to me too but I wasn't sure.

This may well be American sport "lingo". One of the problems that different cultures have while speaking the same language is that they may use what seems to make complete sense to them but means nothing in other countries. For a non-native to spot this is pretty good.