You'll need to know your friend's exact username to be able to find them in the app. On Kik, your username is your ID and it's unique to you. It's how your friends find you and how we connect you to your friends.
Searching by a name, instead of username, would give you lots of matches, making it tough to find the specific person you're looking for. By searching for a username, the only result will be the person you're looking for.
On older versions of Kik, or on Windows Phone, Symbian or BlackBerry, you can use Address Book Matching.