I have a magnetometer which I am using for orientation purposes. What i would like to know is how to calculate the total error when finding the magnitude of the magnetic field vector. So I know each individual axis is accurate to within +-10nT, but how does this propagate to the total magnetic field.

The magnitude of the magnetic field vector is $\sqrt{B_x^2+B_y^2+B_z^2}$, so initially i thought the error would be $\sqrt{dB_x^2+dB_y^2+dB_z^2}$ where $dB_x$ is the error on x axis, $dB_y$ on y axis and $dB_z$ on Z axis. Is this correct?

Your equation ( $e_m = \sqrt{e_x^2 + e_y^2 + e_z^2}$) is the absolute error in the magnitude (so divide by the magnitude to get the % error).