What is the quickest way to evenly slice chicken breasts for jerky?
Freeze the breasts, then use a mandoline to make even slices. (If you have access to a deli slicer with its rotary blade, that would be even faster; however, a mandoline slicer is more typical in a home kitchen.)

The freezing keeps the relatively small pieces of meat stable so they will slice more evenly. Frozen breasts slice more evenly even by hand in my experience.