The signatures of energy release and energy transport for a kink-unstable coronal flux rope are investigated via forward modelling. Synthetic intensity maps are generated from a 3D numerical simulation. The CHIANTI database is used to compute intensities for three Hinode/EIS emission lines that cover the thermal range of the loop. The intensities at simulation resolution are spatially degraded to the Hinode/EIS pixel size (1"), convolved using a Gaussian point-spread function (3"), and exposed for a characteristic time of 50 seconds. The synthetic images generated for rasters (moving slit) and sit-and-stare (stationary slit) are analysed to find the signatures of the twisted flux and the associated instability. We find that there are several qualities of a kink-unstable coronal flux rope that can be detected observationally using Hinode/EIS, namely the growth of the loop radius and the increase in intensity towards the radial edge of the loop. However, EIS cannot resolve the small, transient features present in the simulation, such as sites of small-scale reconnection.