You may want to locate your deep litter chicken run over your intended garden area - that would be the fastest, easiest way to add nutrients and organic material in a hurry.I could use all the compost I can get right now! We are new construction on what was wheat field until this year so the ground desperately needs some organic matter before the garden goes in.
If you have the space, I’ve always dreamed about a setup with a coop in the middle, garden on one side, chicken run on the other…then every fall, switching the run/garden to the other side.