1. Use both daycares.
There are two daycares, if you didn't already know. One in the Battle Resort's south side, and one on the route next to Verdanturf Town. Now, I suggest using the Battle Resort's, because there is a 'sweetspot' that lets you hold down the d-pad and keep going in a continuous square. If needed, I will show you.
Talonlame, which evolves from Fletchling, is a great Flame Body breeding supporter. Put it at the front of your party, and switch around the eggs once they have hatched so that each egg gets the Flame Body. Also, it can make use of the move 'Fly', which lets you move around the world freely.
3. Other tips.
Once you hatch an unsuccessful egg, immediately put the baby in the PC. Don't waste time wonder trading it. Also, use O-Powers a lot, to level them up.
All of these tips come from experience and from other tips. Good luck on your breeding!