  We perform the first magnetic field strength survey of Class I and Flat
Spectrum (FS) sources using $K$-band observations with iSHELL. We obtained new
observations of 42 Class I and FS sources and additionally included 10 sources
from the archive. We detect photospheric lines in 44 of the sources, in
addition to Br$\gamma$, H$_2$, and CO emission in several objects. We model the
photospheric absorption lines of 32 Class I and FS sources and measure their
magnetic field strengths, $K$-band temperatures, gravities, projected
rotational velocities, and infrared veiling values. We put the physical
properties of Class I and FS sources in context by comparing them to the values
derived for a sample of Class II sources. We find that a) the average magnetic
field strength of Class I and FS sources $\langle B \rangle=2.0\pm0.15$ kG is
consistent with the average magnetic field strength of Class II sources
$\langle B \rangle=1.8\pm0.15$ kG, and b) the average gravity of Class I and FS
objects $\log{g}=3.43\pm0.07$ is lower than the average gravity of Class II
sources $\log{g}=3.75\pm0.04$, although there is significant overlap between
both gravity distributions. Furthermore, using stellar evolutionary models, we
deduce that Class I and FS sources have a median age of $\sim$0.6 Myr, and are,
as a group, younger than the Class II stars with a median age of $\sim$3 Myr.
Our results confirm that Class I and FS sources host strong magnetic fields on
their photospheres. Thus, it is likely that these sources accrete disk material
through a magnetosphere similar to the more evolved T Tauri stars.
