[PatK]

brightens the scene up, but then regrets it and darkens it again, then brightens it again and so on

You're right in that I would have said check your 'TV's dynamic brightness', but it appears you have. Next suggestion would be the gfx engine and it's settings (there is nothing within Kodi that plays disco with colours/brightness) so I suspect the graphic card. Set Kodi up using limited colours and colour management profiles and see if there's any relief, failing that switch over to software rendering. What kind of gfx hardware do you have, a debug log might be useful.

P.S. very remote possibility of a cabling problem.