  Flow-induced instabilities are relevant for the storage and dynamics of
magnetic fields in stellar convection zones and possibly also in other
astrophysical contexts. We continue the study started in the first paper of
this series by considering the stability properties of longitudinal flows along
magnetic flux tubes. A linear stability analysis was carried out to determine
criteria for the onset of instability in the framework of the approximation of
thin magnetic flux tubes. In the non-dissipative case, we find Kelvin-Helmholtz
instability for flow velocities exceeding a critical speed that depends on the
Alfv{\'e}n speed and on the ratio of the internal and external densities.
Inclusion of a friction term proportional to the relative transverse velocity
leads to a friction-driven instability connected with backward (or negative
energy) waves. We discuss the physical nature of this instability. In the case
of a stratified external medium, the Kelvin-Helmholtz instability and the
friction-driven instability can set in for flow speeds significantly lower than
the Alfv{\'e}n speed. Dissipative effects can excite flow-driven instability
below the thresholds for the Kelvin-Helmholtz and the undulatory (Parker-type)
instabilities. This may be important for magnetic flux storage in stellar
convection zones and for the stability of astrophysical jets.
