The nRF51822 EK (evaluation kit) is an older kit that uses the second revision of the nRF51822.
The nRF51 DK uses revision 3 of the chip, which comes with some bug fixes and additional features. Also, the kit itself is updated with standard Arduino headers, and supports programming of external boards using the debug out connector (P19).
Programming external boards with the nRF51DK should be as easy as connecting the external board to the DK (and making sure it is powered). Once the DK sees that an external board is connected (by using the ground detect pin) it will move over the debug interface from the nRF51 chip on the DK to the external port.
