What size chuck key do I need for my Black & Decker DNJ62 drill?
13mm / 1/2" refers to the size of the chuck which is also the maximum size bit, though there are some larger bits specifically designed to fit in a 1/2" drill, with a 1/2" shank and a larger tip.

There are plenty of "universal" chuck keys available, which may be the best way to go. But you should be OK with a 1/2" chuck key.