How to burn arduino bootloader on SAMD21 chips using J-Link mini
The Atmel EDBG would work for Arduino Zero since that has the EDBG chip. With Jlink, you can use Atmel Studio. Once the Jlink is connected to the chip via the 10 pin SWD header, goto the programmer option in Atmel Studio, select the chip and programmer and burn your firmware with the selected programmer. You can follow a tutorial here which walks through it.