'becoming cloudy' is correct and can be used in written English.
You can use it to describe the changing weather, for example: It had been a warm and sunny afternoon but the sky was quickly becoming cloudy.
TV Sky Sports 1 HD, 9pm-5am Start of play: 9.30pm Weather Warm and sunny, becoming cloudy later.
Mr. Judson's mission was financed by wealthy Iowans who built their homes around an artificial lake that was becoming cloudy.
Previous experience indicated that adding soil-derived particles to cell culture media frequently resulted in the media becoming cloudy within 24 hr because of introduced viable organisms, but that either heat or alcohol pretreatment of the particles prevented this problem.
Do not allow your amber to sit and dry off on its own, or you risk it becoming cloudy.
Titrate the silver nitrate from a burette or a small syringe to the aquarium sample until the solution stops becoming cloudy.
The housing market is in an unrelenting state of decline, with uncertainty growing over how much further credit markets will tighten, and the outlook for the economy is becoming cloudier by the day.
I wanted so badly to believe that the reality of the situation was becoming cloudier and cloudier to me.
Winters are mild and usually start sunny, becoming cloudier towards February; the occasional cold front brings strong, cooling winds from the north.
In wartime, blame becomes cloudy.
Mix until the water becomes cloudy.
WEATHER They pulled this one out of a hat: Sprinkles, then patchy fog, then cloudy, gradually becoming mostly sunny with a high of 72, but with a chance of showers again by nightfall.
