We have exactly the same issue. Despite not using a lot of fats and scrupulously treating greasy pans with best quality detergent before rinsing, we get a fatberg ever year or so. It's well north of the washing machine outlet so the source is either the kitchen sink or the dishwasher. On the latter we've tried powders and liquids with no apparent difference to the berg.
Part of the problem may be a poor fall on the drain
I have taken bits of berg and soaked them for days in acids/caustic soda/alkalis/domestic drain cleaner and it makes no inroads whatever. In fact some make the blockage worse, for example fat and caustic soda react to form a sort of hard soap. I also use natural enzyme cleaning sticks in the u-bends but can't detect a difference.
All that shifts them is the pressure hose with a metal head thingy as recommended above. Last time even that was being defeated somewhere up the drain and I invested in a set of drain rods from Screwfix. With the metal screw end that broke it up and several long fatberg baguettes flushed through.
Quite satisfying to see it coming through but it's amazing how much builds up in a few months.
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Fatberg in domestic environment 
Fatberg in domestic environment 