Rainbowmons are awarded to me randomly, and currently the only thing I really know what to do with them is to train my other monsters with them.
Is there something else I should be doing with these guys?
Rainbowmons are used to evolve your monster.
As you may have noticed, they are awarded already at max level :
lvl 20 for 2star
lvl 25 for 3star
lvl 30 for 4star
It means that you have to Evolve this rainbomonws (by making them respectively 3star, 4star and 5star) and then use them to evolve your actual monsters at a higher rank.
Example : you have a lvl 25 3star fairy, and 3 rainbowmons lvl 20. You evolve all these rainbowmon to 3stars by feeding them 2stars, and then you feed all the rainbowmons to your fairy so she becomes a 4star.
If these explanations are unclear, tell me, I'll try better!