chicken
鷄 centers on the domestic chicken as a bird. It is a specific character for chicken, often used in older or formal contexts.
鷄 combines 奚 (which likely contributes the sound) with 鳥 (bird) to specify a chicken. The exact role of 奚 is uncertain, but the character is a phono-semantic compound for chicken.
The left side 奚 looks like a hand over a tied-up bird, and the right side 鳥 is a bird. Picture a chicken being held by its legs: 鷄 is a chicken.
For ケイ, imagine a chicken laying an egg shaped like the letter K: K -> ケイ, and the chicken clucks proudly.