Hi! This tutorial will be short and easy. As always, let's have a look on result we will get.
Create seven equal stripes...
... and decorate them.
Align and distribute.
I added some starts.
Now let's group all the objects...
... and rotate them to make all composition horizontal.
Here is the culmination! Go to "Object - Envelope Distort - Make with Warp".
Dialog window will appear. You can choose here any style for your rainbow. I selected "Flag" style. You can get different variations of the shape by changing "Band" and "Distortion" value.
Finished!
I hope this tutorial was helpful.
Thank you for reading this and good luck!