There don’t seem to be any animals that seek out clouds as a habitat. While it’s easy to imagine active flyers such as birds, bats and insects using clouds to hide from predators or prey, evidence that they do is lacking.
Indeed, the poor visibility might be a good reason to avoid them. Same for all the water droplets and ice crystals, which might make flying difficult.
Then there is the weather and electrical activity associated with clouds. Even large birds can come a cropper in a storm and tend to steer clear.
However, streaked shearwaters have been tracked flying straight through the centre of cyclones.