  We examine the thermal free-free millimetre fluxes expected from non-dusty
and non-pulsating K through mid-M giant stars based on our limited
understanding of their inhomogeneous chromospheres. We present a semi-analytic
model that provides estimates of the radio fluxes for the mm wavelengths (e.g.,
CARMA, ALMA, JVLA Q-band) based on knowledge of the effective temperatures,
angular diameters and chromospheric Mg II h & k emission fluxes. At 250 GHz,
the chromospheric optical depths are expected to be significantly less than
unity, which means that fluxes across the mm and sub-mm range will have a
contribution from the chromospheric mate- rial that gives rise to the
ultraviolet emission spectrum, as well as the cool molecular material known to
exist above the photosphere. We predict a lower bound to the inferred
brightness temperature of red giants based on heating at the basal-flux limit
if the upper chromospheres have filling factor 1. Multi-frequency mm
observations should provide important new information on the structuring of the
inhomogeneous chromospheres, including the boundary layer, and allow tests of
competing theoretical models for atmospheric heating. We comment on the
suitability of these stars as mm flux calibrators.
