  We consider a recent proposal for a physical realization of the
Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an
irregularly-shaped graphene flake. We study in detail charge transport
signatures of the unique non-Fermi liquid state of such a quantum dot coupled
to non-interacting leads. The properties of this setup depend essentially on
the ratio $p$ between the number of transverse modes in the lead $M$ and the
number of the fermion degrees of freedom $N$ on the SYK dot. This ratio can be
tuned via the magnetic field applied to the dot. Our proposed setup gives
access to the non-trivial conformal-invariant regime associated with the SYK
model as well as a more conventional Fermi-liquid regime via tuning the field.
The dimensionless linear response conductance acquires distinct $\sqrt{p}$ and
$1/\sqrt{p}$ dependencies for the two phases respectively in the
low-temperature limit, with a universal jump at the transition. We find that
corrections scale linearly and quadratically in either temperature or frequency
on the two sides of the transition. In the weak tunneling regime we find
differential conductance proportional to the inverse square root of the applied
voltage bias $U$. This dependence is replaced by a conventional Ohmic behavior
with constant conductance proportional to $1/\sqrt{T}$ for bias energy $eU$
smaller than temperature scale $k_BT$. We also describe the out-of-equilibrium
current-bias characteristics and discuss various crossovers between the
limiting behaviors mentioned above.
