Generally speaking, shiny trades better than non-shiny, so if you can get a shiny flawless jolly or adamant Dragonite, you can clone the egg, then hatch a shiny on yours, and a non-shiny on another game. I recommend doing this for all of them.
Note: Make sure to make everything female if possible. I already have an adamant (I think) male Gyarados, so I'm looking for female
I suggest making several versions of each - Jolly and Adamant Female Gyarados, Jolly, Adamant, and Naive/Hasty? (Mixed) Dragonite (preferably with a useful Hidden Power... HP ice isn't that good on a dragon, but something else...), and probably Adamant and Jolly murkrow.