See above post for night/star skydome.
Recently i had idea for cloudy sky (it can be also done for dusk/dawn scenes).
make sky plain blueish color (or just white/grey)
add to this cubemap with gradient either linear around horizon or bit of circular for spot where sun is
you can use emmisive color or just multiply by light color ets to simulate time of day and sky color
So you should have nice background gradient.
Now we need clouds:
use flat black box and vector field to generate slowly moving clouds. Then camera capture to create grey (alpha mask) texture.
Then use that texture to overlay animated clouds on skydome.
Or just make huge vector field (big voxels, not huge number of them) and animate clouds with that field.
If you want plain 4k texture for sky you need to render it in your favorite 3d app. Look for tutorials about skydomes in maya, blender, max.
When you have texture use that amd tool to create cubemap. And be warned that 1024x1024 texture is 6 textures 1k by 1k. So 4k cubemap texture will be around 300mb uncompressed, if not more.
Ps. I did not made/tested that sky idea, so it may be hard to do or not working in unreal etc.