Hi Georgia,

I could not find any research on this topic but I have some insights from other people who have raised chickens. You can feed chickens japanese beetle killed with soapy water under a couple conditions. Try to use a milder soap (e.g. castille soap). If you must use something like dishwasher soap, make sure that the mixture is very diluted. After drowning the beetles in soapy water, transfer them to a container of regular water to wash out the soap still on/inside them. You may have to do multiple rounds of this "rinsing" to remove the soap residues, seeing less and less soap bubbles in the water each time. While it won't kill your chickens if they ingest some soapy water, it may give them diarrhea. You can use vegetable oil in place of soap, but I would still "rinse" the beetles after killing them. 

If possible, I recommend killing japanese beetles without soapy water. Rather than a bucket, find a plastic or glass container with slick walls that the beetles cannot climb. A taller container will make it harder for the beetles to climb out. You can fill it with water, or not. Beetles collected this way will be much safer for your chickens.

Let me know if you have further questions.