  We analyze the possibility of primordial magnetic field amplification by a
stochastic large scale kinematic dynamo during reheating. We consider a charged
scalar field minimally coupled to gravity. During inflation this field is
assumed to be in its vacuum state. At the transition to reheating the state of
the field changes to a many particle/anti-particle state. We characterize that
state as a fluid flow of zero mean velocity but with a stochastic velocity
field. We compute the scale-dependent Reynolds number $% Re(k)$, and the
characteristic times for decay of turbulence, $t_{d}$ and pair annihilation
$t_{a}$, finding $t_{a}<< t_{d}$. We calculate the rms value of the kinetic
helicity of the flow over a scale $\mathcal{L}$ and show that it does not
vanish. We use this result to estimate the amplification factor of a seed field
from the stochastic kinematic dynamo equations. Although this effect is weak,
it shows that the evolution of the cosmic magnetic field from reheating to
galaxy formation may well be more complex than as dictated by simple flux
freezing.
