  A measurement of primordial non-gaussianity will be of paramount importance
to distinguish between different models of inflation. Cosmic microwave
background (CMB) anisotropy observations have set unprecedented bounds on the
non-gaussianity parameter f_NL but the interesting regime f_NL <~ 1 is beyond
their reach. Brightness-temperature fluctuations in the 21-cm line during the
dark ages (z ~ 30-100) are a promising successor to CMB studies, giving access
to a much larger number of modes. They are, however, intrinsically non-linear,
which results in secondary non-gaussianities orders of magnitude larger than
the sought-after primordial signal. In this paper we carefully compute the
primary and secondary bispectra of 21-cm fluctuations on small scales. We use
the flat-sky formalism, which greatly simplifies the analysis, while still
being very accurate on small angular scales. We show that the secondary
bispectrum is highly degenerate with the primordial one, and argue that even
percent-level uncertainties in the amplitude of the former lead to a bias of
order Delta f_NL ~ 10. To tackle this problem we carry out a detailed Fisher
analysis, marginalizing over the amplitudes of a few smooth redshift-dependent
coefficients characterizing the secondary bispectrum. We find that the
signal-to-noise ratio for a single redshift slice is reduced by a factor of ~5
in comparison to a case without secondary non-gaussianities. Setting aside
foreground contamination, we forecast that a cosmic-variance-limited experiment
observing 21-cm fluctuations over 30 < z < 100 with a 0.1-MHz bandwidth and
0.1-arcminute angular resolution could achieve a sensitivity of order
f_NL[local] ~ 0.03, f_NL[equilateral] ~ 0.04, and f_NL[orthogonal] ~ 0.03.
