Is it gray sky or grey sky?

Whether you write gray sky or grey sky depends on which variant of English you use. In American English, the standard spelling is gray, so you would write gray sky. In British English, Australian English, Canadian English, and many other Commonwealth varieties, the standard spelling is grey, so you would write grey sky. Both spellings refer to the same color and are correct within their respective dialects, so neither is wrong, it is a matter of regional preference and consistency. If you are writing for an American audience or following American style guides, use gray sky. If you are writing for a British, Australian, or Canadian audience, use grey sky. Many people use both interchangeably in informal writing, but for formal writing, consistency with your chosen dialect matters. The phrase describes an overcast sky that appears dull and cloud-covered, often associated with gloomy weather, and both spellings convey that image accurately.