All schools and many work places lock down social internet sites (and other ones) so that students/workers can't spend all their time chatting with their friends, it's a pain, I get that.
One option you may want to look into is something called a VPN or virtual private network. It will require some technical knowledge to get setup, but instructions are easily available on the web.
This may not be the best option in a school setting though, as getting caught trying to circumvent school's security system may get you in trouble.
Another way to use Kik at school is to try to get an unlimited data plan, if you are in the UK, the three network is ideal for this. Even on pay as you go.
The benefits on NOT using Kik at school
The main plus side is that at least the school won't be able to read all your messages etc. Which they may have access to if you go through their wifi. I have even heard of people being sent a bill for accessing non-educational sites, though I don't know if that would be enforceable.