As for Golden Chickens, you need to get a Golden Egg first and put it in the Incubator. To do this, you need to first get 100% Perfection in the game, which is nearly endgame-level content.

A very rare and special egg with a solid gold shell. Golden Eggs are an animal product gathered from Golden Chickens. Once this is done, you can then purchase 1x Golden Egg for 100,000g from ...

Golden Comet chickens are known for their prolific egg-laying abilities ... so you will probably need an incubator to hatch ...