Mine will consume almost all insect fare, with exception of insects that have red on them. Insects with red here typically use compounds they collect from milkweed to keep predators at bay.
We don't get many Japanese beetles here in my yard, but the girls sure do snap them up quickly when the do see them! The go to town in stink bugs, too!
May through June in some years I have placed a light near roost of young game chickens. Night flying insects (May Beetles mostly) then come into range where chickens can pick them off from their roost. Some nights allow for very rapid crop fill. This seasonal and not well suited for feeding more than a few birds at a time.
When working on beehives some of the chickens follow me and wait for me to drop burr comb. They consume the drone brood very well. I also have been throwing scratch at base of beehive to encourage chickens inspecting area for insects. Hope is to use that as a measure for controlling hive beetles in and just before the pupal stage.
At work I have a lot of ponds and a river nearby where mayflies (burrowing mostly) emerge in mass. Chickens really like those.
Recently I have begun exploring the use of mass harvested Japanese Beetles as eats. The beetles do not keep well outside of a freezer so working on ways to increase their density and dry them so they can be kept year round. Below is an ongoing thread working on the procedure.
https://www.backyardchickens.com/threads/making-feed-from-japanese-beetles.1223688/