It's traditional "baby talk," or, if you prefer, "child-directed speak" or "motherese." It's a kind of affectionate babble-like sound parents make to their children. Long before children start to form words and discover grammar, they must first learn that sounds communicate. For some reason, "itchy kitchy koo" is a kind of standard example, just as "Hip! Hip! Hooray" is the traditional example of a cheer, or "Bow wow!" is the tradition rendering of a dog's bark. Just making this up--a longer example might go something like this: "Ooooh woooh woooh! Ickle ickle ickle ooo my sweetie izzums, izzy? Yes he IS! Yes he IS! He IS! He IS! He IS! Is IS? He is! Izzy izzy izzy-kins! And does 'e wuv his da-da? He does, he does! Does he wike to be tickle-ickle-ickled? Tickle-ickle-ickle! Woo woo woo!"

Well, I'm not sure this will help or if there's a Chinese equivalent, but it doesn't actually mean anything! It's something people say to babies. So...it's just nonsense "cutesy" baby-talk. I guess you could call it an interjection... But whereas interjections are usually made to no one in particular (or are directed 'at' the general situation), "kitchee kitchee koo" would be said TO a baby. I doubt it's something you're likely to come across very often in reading though.

Also, I am CERTAIN that "baby talk" exists in every language. The right "translation" would be to translate it into any kind of Chinese "baby talk." Just imagine the most typical thing that a Chinese mother says to a very young baby, and use that.