Okay, well, first, I would point you to some guides on the forums that have advice on making rainbow decks:
http://elementscommunity.org/forum/deck-help/how-to-build-an-effective-rainbow-deck/Even though this one is old, it's still relatively relevant.
Anyways, as for your rainbow deck, try to limit your cards. Because of the amount of
cards you're using, that's most likely going to be the best mark to use. This means that using HGs is a bit more challenging, so you'll want a smaller deck that doesn't rely on them. You can (and should) include some in your rainbow, but try to not make them be something you have to depend on, since without a
mark, it's unlikely you'll be drawing an extra card each turn.
So, you'll probably want some Supernovae in there, and I would suggest either increasing the amount of Cockatrices or dragons, I'm not entirely sure which one you're meaning to use Mitosis on. Either works, although in a rainbow, Cockatrice would probably be better for quanta purposes. At that point, a few Shards of Readiness would be helpful (although if you don't have any, that's fine, it'll still work).
Then just fill up the remaining cards with supporting cards from the other elements. For example, your deck has no PC and very limited CC, so you'll want to change that. You might want to include Deflags and Lightnings for that. just think about what things your deck doesn't have and compensate for it. There's still quanta protection, quanta control, protection from PC and CC, healing, deck-out prevention, etc. Just keeping testing and find what you think is the best. This is where Trainer is especially helpful, since you have all the cards to build your deck from.
