Could it be:
>! Rain

I come from a cloud.
>! Clouds are made of water which will fall down as rain.

Some long streaks of light
And a glowing shroud.
>! Clouds (the shroud) can glow, and sometimes when they have holes, you see streaks of light come from them.

But now out of sight.
>! As rain in the sky, it is not easy to see in comparison to clouds.

Seen in the summer,
>! It can rain quite frequently in summer (depending on your location)

Despite my nickname.
>! Fluffy the cloud.

Many deaths occurred,
>! Many deaths can occur from floods (or excess rain), or the 'reign' of a bad ruler.

But I'm not to blame.
>! I guess we just have to blame mother nature!