To keep flat on a grill:
Make a depression or divot about ½ inch deep in the center of your patty to help your burger cook flat instead of puffy. The puffiness is caused by fat and connective tissue in the meat. Trust me, the divot works to make the patty flat!
To divide equally:
Divide the total weight of the burger meat you have by the number of patties you want to make, then mound that weight on your kitchen scale. Every burger will be the same size.