Here’s my take on this, as recovering deleted data can be approached in a couple of ways.
Your most reliable method is restoring from a recent iCloud or iTunes backup, provided one was made before the messages were deleted. The major pro here is that it’s a built-in function and likely to work. The con, however, is significant: you’ll have to restore your entire iPhone to the state of that backup, potentially losing any new data you’ve added since then.
On the other hand, you have third-party recovery software. These tools are designed to scan your device for traces of deleted data and allow for more selective recovery. The upside is you might be able to retrieve just the Kik chats without a full system restore. The downside is that success isn’t guaranteed, as the data can be overwritten by new activity on your phone.