We present a multiwavelength study of the AGN-host starburst galaxy PKS 0529-549 at z 2.6. We use (1) new ALMA observations of the dust continuum and of the [C I] 370 µm line, tracing molecular gas, (2) SINFONI spectroscopy of the [O III] 5007Å line, tracing ionized gas, and (3) ATCA radio continuum images, tracing synchrotron emission. Both [C I] and [O III] show regular velocity gradients, but their systemic velocities and position angles differ by ∼300 km s −1 and ∼30 • , respectively. The [C I]is consistent with a rotating disc, aligned with the dust and stellar continuum, while the [O III] likely traces an outflow, aligned with two AGN-driven radio lobes. We model the [C I] cube using 3D disc models, which give best-fit rotation velocities V rot 310 km s −1 and velocity dispersions σ V 30 km s −1 . Hence, the [C I] disc has V rot /σ V 10 and is not particularly turbulent, similar to local galaxy discs. The dynamical mass (∼10 11 M ) is comparable to the baryonic mass within the errors. This suggests that baryons dominate the inner galaxy dynamics, similar to massive galaxies at z 0. Remarkably, PKS 0529-549 lies on the local baryonic Tully-Fisher relation, indicating that at least some massive galaxies are already in place and kinematically relaxed at z 2.6. This work highlights the potential of the [C I] line to trace galaxy dynamics at high z, as well as the importance of multiwavelength data to interpret gas kinematics.