How can I make a peeling paint effect?
The basics of this can be pretty easy if you want it to be. Getting the exact desired effect, much like anything in crafting, will take some experimentation. 

In its simplest form put down you base paint i.e. the colour you want to see below the peeling, distress and etc. Then put down something to help prevent the next layer of paint from binding. White glue works well for this. You would not necessarily use glue on your entire surface but where you want the cracking / peeling to occur. In your case you can try and target it along a line to simulate broken wall or foundation or something. How long you let the glue dry before you put on the next layer of paint is subjective. Most seem to wait until it is tacky to the touch. 

Next you would put on your top layer of paint. The choice of paint should not matter here to much either. A milk paint lends easier to distressing or chipping. You see milk paint used a lot in "antiquing" furniture. 

Once that paint is dry it should have cracked on its own while drying. If that is not to your satisfaction you could use some tools to help it along. Utility knives, putty knives would be obvious tools of choice. Again, you would need to experiment to get your desired effect. 

Aside from the above or possibly in conjunction I have also seen people accelerate the drying process with something like a heat gun / hair dryer. This will definitely help the peeling process via bubbling. Take caution as to not burn or melt the paint.