Tried passing my DisplayCAL ICC profile into Kodi colour management but couldn't get a result I was happy with - obviously messed up gamma curve etc.
Instead, I used the 3DLUT Maker tool included with DisplayCAL to produce a .3dlut file, and put Kodi into 3DLUT mode (as opposed to ICC Profile).
3D LUT should be configured as in the screenshot above, and then point Kodi to the .3dlut file.
You might need to enable the 'use limited colour range' setting in Kodi - I found I did need this for one machine, but not for another, despite both using PC monitors, and both behaving identically in other applications (colour managed or not). Refer to these Basic Settings patterns.