Here's an old-school simulation of flying into clouds.
This is resource-heavy due to all the PNGs, but it demonstrates the concept. To more easily make out the different layers and how they scale and change positions, move the time cursor manually to speed things up.
SkyFloat.hype.zip (2.4 MB)
A variation that I've used in AE video projects is to simulate a moving landscape below. For that I would take a high-resolution high-alititude photo of the ground, select a long swatch, place it inside a mask to create a horizon, rotate it along the X and then animate it along the Y. For depth, I created a haze layer with an opacity gradient from zero at the halfway point to around 20% white at the top. To complete the illusion, add a strip of blurry clouds on the horizon. As for the blue background, use a gradient that gets darker towards the top.