All data are based on minecraft.gamepedia.com/Chicken and many tests with 5 different chicken farms and having 8 chickens in each one, I got these results
The values of my farms are tested and are not random values
I try to make the values real
Every 30 sec (600 ticks) there is a 50% chance of giving you a cooked chicken.

Instructions:
Put a dropper facing up, above the dropper put a white_carpet, on the dropper side put an item_frame and in the item_frame a cooked_chicken, and voila!

Now you will have your portable cooked chicken farm.