Minecraft – How do the eggs function

All animals do spawn naturally. If you are having trouble getting them to spawn, I suggest trying this:

As the world is not infinite (not unlimited world area) , an interesting new game mechanic called "animal spawn control" can be used. This includes removing or covering all dirt blocks on the surface of the world (and therefore the grass blocks) except in a small area to control where animals spawn. It will also increase their spawn rate.

Credits to the Minecraft Wiki - Pocket Edition: http://www.minecraftwiki.net/wiki/Pocket_Edition

As Alice Rees said, more chickens. Or more patience, that works too. There isn't anything that makes them lay eggs more often.

At some point the breeding feature will be added to Pocket Edition – that will make chicken farms much more productive, since breeding chickens together increases their population much faster than waiting for them to lay eggs and then hoping it will spawn a baby chicken when thrown. But until the breeding feature is added, you simply have to wait, and patiently build up your chicken population. If you let your chicken population get large before slaughtering any, you'll eventually have so many that you'll be swimming in chicken eggs and can set up a separate food-chicken pen from your egg-laying pen, but it takes a while to get there.