I seriously doubt wheel size has anything to do with puncture or flat prevention.
Common causes for flats are sharp objects, or in the case of snake bites, a pressure too low for the activity (type of riding).
In the case of sharp objects, they penetrate the tire casing because, for a moment, all the weight applied to the wheel is pressed against a tiny surface (for example a nail's tip), and the pressure surpasses the tire's structural resistance. Remember pressure is measured in force per area unit, so lets say you apply 50 pounds of weight to the front tire, and that the tire is a slick one inflated to 50 psi (pounds per square inch). Now the contact patch on a smooth surface will have roughly one square inch. Now roll the tire over a sharp nail tip, of surface (1/32 x 1/32 = 0.00098) square inch. This is a pressure equivalent to 51,200 psi (50/((1/32)^2). This tremendous pressure is enough to break the tire casing structure, so the object punctures it.
Now, if you change the size of the wheel, or only the tire size and apply the same 50 pounds of weight over the same nail, the pressure on the contact point will still be the same, since the nail's size is unaffected.
Instead of wheel size, many other variables can make a tire more or less puncture prone, for example thickness, thread count, rubber grade, structure. Some tires are purposely made to be puncture resistant, others are just like a thick(ish) balloon.
Some tires can escape puncture situation just because circumstances, for example a knobby tire that is penetrated by a sharp but short object. The object is so small that it doesn't get to the tube.
In the case of snake bites (a.k.a. Pinch flats), thick and hard casings tend to resist a little more, but they are not invincible. Always check tire air pressure before riding, and if you ride low pressure intentionally, ride accordingly: don't hit sharp edges and absorb shock with your arms and legs.
If you are suffering constant punctures, consider buying puncture proof tubes or specially belted tires, but also examine your path choices. If you are riding on the street, don't ride the gutter, because there is where all the trash accumulates (shredded glass, wire from overly worn car tires, etc.)
By the way: the effective size difference between 700c and 27" is only 4 millimeters, check Sheldon Brown's article on tire sizing: enter link description here. Changing a bike wheel size may just be a hassle, with no benefit at all.