  We investigate the conditions under which the fluting ($m = 2$), $m = 3$, and
$m = 12$ magnetohydrodynamic (MHD) modes in a uniformly twisted flux tube
moving along its axis become unstable in order to model the Kelvin--Helmholtz
(KH) instability in a twisting solar coronal hole jet near the northern pole of
the Sun. Using a twisting jet of 2010 August 21 by \emph{SDO}/AIA and other
observations of coronal jets we set the parameters of our theoretical model and
have obtained that in a twisted magnetic flux tube of radius of $9.8$~Mm, at a
density contrast of $0.474$ and fixed Alfv\'en Mach number of ${\cong}0.76$,
for three MHD modes there exist instability windows whose width crucially
depends upon the internal magnetic field twist. It is found that for the
considered modes an azimuthal magnetic field of $1.3$--$1.4$~G (computed at the
tube boundary) makes the width of the instability windows equal to zero, that
is, it suppress the KH instability onset. On the other hand, the times for
developing KH instability of the $m = 12$ MHD mode at instability wavelengths
between $15$ and $12$~Mm turn out to be in the range of $1.9$ to $4.7$~minutes
that is in agreement with the growth rates estimated from the temporal
evolution of the observed unstable jet's blobs in their initial stage.
