Context. Galaxy mergers are an important and complex phase during the evolution of galaxies. They may trigger nuclear activity and/or strong star forming episodes in galaxy centres that potentially alter the evolution of the system. Aims. As part of the guaranteed time observations program Mid-Infrared Characterization Of Nearby Iconic galaxy Centers (MICONIC), we used the medium-resolution spectrometer (MRS) of the Mid-Infrared Instrument on board the James Webb Space Telescope (JWST) to study NGC 6240. We aim to characterise the dual active galactic nuclei (AGN), the ionised gas outflows, and the main properties of the interstellar medium over a mapped area of 6.6″ × 7.7″. Aims. We obtained integral field spectroscopic mid-infrared data (wavelength from 4.9 to 28 μm) of NGC 6240. We modelled the emission lines through a kinematic decomposition that accounts for the possible existence of various components. Methods. We have resolved both nuclei of NGC 6240 for the first time in the full 5- 28 μm spectral range. The fine structure lines in the southern (S) nucleus are broader than for the northern (N) nucleus (full width at half maximum of ≥1500 versus ~700 km s^{- 1} on average, respectively). High excitation lines, such as [Ne V], [Ne VI], and [Mg V], are clearly detected in the N nucleus. In the S nucleus, the same lines can be detected but only after a decomposition of the polycyclic aromatic hydrocarbon features in the integrated spectrum, due to a combination of a strong mid-IR continuum, broad emission lines, and intense star formation (SF). The SF is distributed all over the mapped field of view of 3.5 kpc × 4.1 kpc (projected), with the maximum located around the S nucleus. Both nuclear regions appear to be connected by a bridge region that is detected with all the emission lines. Based on the observed MRS line ratios and the high velocity dispersion (σ ~ 600 km s^{- 1}), shocks also dominate the emission in this system. We detected the presence of outflows as a bubble north-west from the N nucleus and at the S nucleus. We estimated an ionised mass outflow rate of 1.4 ± 0.3 M_⊙ yr^{- 1} and 1.8 ± 0.2 M_⊙ yr^{- 1}, respectively. Given the derived kinetic power of these outflows, both the AGN and the starburst could have triggered them.