  Hypernovae powered by magnetic jets launched from the surface of rapidly
rotating millisecond magnetars are one of the leading models to explain
broad-lined Type Ic supernovae (SNe Ic-BL), and have been implicated as an
important source of metal enrichment in the early Universe. We investigate the
nucleosynthesis in such jet-driven hypernovae using a parameterised, but
physically motivated, approach that analytically relates an artificially
injected jet energy flux to the power available from the energy in differential
rotation in the proto-neutron star. We find ejected $^{56}\mathrm{Ni}$ masses
of $0.05\,\mathrm{M}_\odot - 0.45\,\mathrm{M}_\odot$ in our most energetic
models with explosion energy $>10^{52}\,\mathrm{erg}$. This is in good
agreement with the range of observationally inferred values for SNe Ic-BL. The
$^{56}\mathrm{Ni}$ is mostly synthesised in the shocked stellar envelope, and
is therefore only moderately sensitive to the jet composition. Jets with a high
electron fraction $Y_\mathrm{e}=0.5$ eject more $^{56}\mathrm{Ni}$ by a factor
of 2 than neutron-rich jets. We can obtain chemical abundance profiles in good
agreement with the average chemical signature observed in extremely metal-poor
(EMP) stars presumably polluted by hypernova ejecta. Notably, $\mathrm{[Zn/Fe]}
\gtrsim 0.5$ is consistently produced in our models. For neutron-rich jets,
there is a significant r-process component, and agreement with EMP star
abundances in fact requires either a limited contribution from neutron-rich
jets or a stronger dilution of r-process material in the interstellar medium
than for the slow SN ejecta outside the jet. The high $\mathrm{[C/Fe]}\gtrsim
0.7$ observed in many EMP stars cannot be consistently achieved due to the
large mass of iron in the ejecta, however, and remains a challenge for
jet-driven hypernovae based on the magneto-rotational mechanism.
