Kilik isn't built for punishment, in fact he isn't an easy character to play beyond the whole "Let's spam moves!" stage.
I'd advice you to keep your punishment options limited to 3 (this applies to all characters)
Light punisher, Standard Punish and Heavy Punisher.
For Kilik
Light - 46B/6AA depending on range
Standard - 66B
Heavy - 3kB
You also have to keep one or two moves at the back of your head for whiff punishing.
For Kilik, these would be 4 or 22B. Application of whiff punishers are kinda obvious, provided you know what's whiffing?
As for what type of punishment to use, when you block a move (hence forth known as 3B.. Just an example, easier to type than "that move). Try 66B first, Its the safest option, and does decent damage. Three scenarios stem out from here.
1. If its not fast enough to punish 3B, keep that in mind. The next time you block 3B, try 46B. If that STILL doesn't punish. Kilik can't punish 3B, you now know this. So the next time the opponent does 3B, you can force a mixup when you block 3B. Like maybe. 2K/Throw and 66B.
2. It CAN punish 66B. So now you know it's bad enough on block for a 66B. The next time you can block 3B, you can try 3kB. If it hits, it hits. If not. Depending on your outcome, remember which punishment option is better to punish 3B and use it accordingly.
3. When you try to 66B your opponent's 3B. You get hit by hit 2nd attack on counter hit! That's not supposed to happen! Well, in this scenario, it means that the opponent's 3B is either + on block, or that it only has a small disadvantage on hit. How do you confirm this?
When you block 3B again, you can take the risk to 6AA or 46B. If those counterhit your opponent's 3B, that means that the advantage/disadvantage of 3B on block isn't large/small enough for the opponent to beat out Kilik's 46B. You can use this to prevent them from taking the offense when you block their 3B, and forces your opponent to BLOCK. Of which you can mixup and put a bit of hurt on him. If your 46B still doesn't beat out his next move, then the frames of 3B on block is really too much for Kilik to handle. You'd have to find another way to deal with his 3B. Like stepping or GI-ing. Simply punishing it off a block is not possible.
I hope this wasn't too complicated to understand XD Let me know if you don't get any part of it.