The SAM chips have ARM cores, so you should look compiliing with
arm-none-eabi-gcc and flashing/debugging with
OpenOCD is a program that communicates with debugging probes for a number of processor/microcontroller architectures, analogous to
avrdude for AVR. You will have to figure out how to configure openocd to talk to your board. A quick google search brought me this guide, which might point you in the right direction, although I don't have a SAM breakout board to verify it with.
OpenOCD is definitely worth learning if you're going to be working with ARM chips, but you could probably also flash your code using Atmel's IDE, Atmel Studio. I shy away from using proprietary IDEs, but if you need to get up and running quickly, you could probably use it to both build and flash your project. Hope this helps.
edit: I glossed over the word "Linux" in the title of your question. I believe Atmel Studio is only available for Windows, so unfortunately you're stuck using the much more versatile open source tools which are available for Linux.