I have been a fan of composting for at least 30 years, learned of composting from my mother- a gardener years prior.
Composting and chickens was a bit if a small challenge for me at first but today I do it like this without a problem as long as I pay attention and except the risk/benefit ratio. Climate ditactes what I can and cannot do and so does space. I am in a warm climate with limited space for chicken, household and yard composting.
My kitchen and chicken waste I use tumblers.
They work terrific. Bugs go in, do their thing, I can turn and aerate and feed as I go until it gets locked down. Chickens eat the bugs that fall out like seargent fly larvae, grubs, roaches yum! One bin cooks while I fill the other. I toss in nesting material, poop, kitchen and then finish it off with horse poop to speed the cooking. It takes me a few months to fill one and a few months for the other to get done cooking as I am over filling them and slowing the process. I obviously need another set of tumblers.
Lock it up, empty the other and then fill the empty. Been doing this for 10 years now (same compost tumbler!) And it is magic. Chooks can't get to anything till I empty it out in a bin for them to dig through. I never add meat, dairy or oils. And I watch my ratios to some extent as bad ratios make slower compost.
I also have a cold compost bin and we compost our horse poop separately. Best stuff ever! This set up is very convenient and controlled. I also periodically add fresh horse poop to my cold compost to help it out and speed it up. To flip that I just lift and move and shovel while the girls pick through. It's just my big green waste so no worries.
How ever and what ever you find to work for you awesome! Composting is the best! Putting all that carbon back into the earth and producing snacks and soil is terrific.