Refers to the appearance of the sky and the likely weather development; often used when the weather looks threatening or changeable.
The weather is starting to look threatening.
Let's check how the sky looks before heading out.
The negotiations suddenly took a turn midway through.
As the meeting went on, things started looking bad.
Let's watch how things develop for a while before deciding.
雲行き literally describes the movement of clouds and figuratively implies an ominous turn of events, while 風向き is more neutral and can describe any shift in mood or trend.
雲行き describes the 'look' or trend of a situation (as in 雲行きが怪しい), while 暗雲 specifically evokes a dark, threatening sign of trouble.