Drawing a cute cartoon rainbow is not a very hard challenge in terms of sketching. All you need to do is create two small clouds and then add six stripes of colors (a real rainbow is made of seven different colors, but since indigo and violet are pretty similar, mine will have only six colors).
However, the real challenge comes from creating nice reflections or adding a genuine gradient effect to the rainbow. Since a rainbow is made of very small drops of water and sunlight, it's not a tangible object that you can hold in your hand. Therefore, it should also look like an organic and shiny object floating into the atmosphere.
Notice in the fourth step how I have added some gradient effect to the rainbow itself and on the background. In the fifth step, a reflection was added to the rainbow (on the left) and on each cloud. Have fun!