Flier Team sugestions

If you want a Flying Tank Catria (+Res/-HP for a true Optimal build) is your girl 100%. So many people (including the "Optimal Builds" on this site) want to build her more offensively then "complain" that she's not as good as others at it - No Sh*t...
Seriously though, I would suggest Elincia/Catria/Sanaki, and Robin.

This gives you a Legendary Hero (for "seasonal" Stat Boosts) good Physical and Res offenses, and a super tank.

Edit note: The IVs on your listed Catria are not great so if you want a team specifically out of your characters listed see others suggestions, but being available at 3-4* means you should be able to get a -HP (any boon will work really I currently have her as +Spd myself) Catria fairly easily to promote and merge.

For red you should go Elincia as the -atk on Caeda is terrible. You could always upgrade another one with good ivs but for now just use elincia.
For blue, a flying mage is always helpful. With +Spd on morgan you could run a good bladetome set and nuke everything. This paired with hone fliers on NY! Azura would be incredible.
For green, NY! Azura. A dancer is always useful and she comes with hone fliers.
Robin is you're only colorless option so that's that. Generally colorless isn't necessary so if you want, you're fourth member could be firesweep shigure. Having a firesweep weapon is always good, especially on a flier team.

You have the units for a pretty good flyer team.

Personally, I would go with:

Azura - Purpose - buff with Hone Flyers and Dance
Elincia - Give her Fortify Flyers. Great attacking unit, and Flyer Formation gives some interesting movement options
Female Morgan - DD seal and Blarserpent plus buffs will make her a great tank vs. mages. C slot can be flyer buff (Goad or Ward Flyers)
Female Robin - Good to kill ranged attackers. Give her Goad or Ward Flyers.

Give Robin, Morgan, and Elincia reposition as assist. (You can use other movement assists like draw back, but reposition is best)

If you want, you can give Morgan a blade tome to take advantage of the +6 to all stats for a massive attack bonus. I don't know that it's really necessary.

My suggestion for an all out offensive team:
Elincia - Amiti, Death Blow, Fortify Fliers
Morgan - Blarblade, Fury/L&D, suitable ploy/Goad Fliers
Cherche - Brave Axe, Death Blow, Goad Fliers, Heavy Blade seal (I just prefer her to her son but they do much the same job)
Azura - For Hone Fliers and singing

Burst damage from the two brave weapons and a nuke from Morgan when buffed. B skills can be Desperation, Vantage for Morgan, Flier Formation or a suitable Chill skill.

Azura could be swapped for Robin if some defense is preferred, she's still fast, her blessing makes her allies faster and adaptive damage is always handy.