Is there a preferred ordered for Cordoba, Granada, & Sevilla - flying in and out of Madrid

Not really. I chose Cordoba to start the closest place.
Are you spending time in Madrid before/after?

High-Seed train times and sequence: Madrid-3.5 hrs-Granada- 1.5 hrs Cordoba- :45- Seville- 2:40- Madrid
This sequence requires no backtracking, as reversing it would.
www.TheTrainline.com

When you travel by train, Cordoba is on the way from Madrid to Seville and from Granada to Madrid. In many/most cases it's on the way from Seville to Granada as well. That isn't obvious from looking at a road map, but it's the way the express rail lines run. Therefore, Cordoba can realistically fall anywhere on this itinerary. There's not a great deal of fast rail service into and out of Granada, so the schedule might be more attractive for one routing than another.

No matter what the order is, I now see you pass through Cordoba two times.

Note that there are only 3 trains each day traveling between Madrid and Granada. One morning train— probably the one to reserve— one afternoon train, one evening train,
Don’t wait to buy your tix since the trains easily could sell out .
Between Seville and Granada, only Renfe does this route in less than three hours and tickets are about $55.
The Alsa bus company runs this route in about 3 hours for $27 . And there are a lot more buses scheduled than trains.

www.Busbud.com
www.TheTrainline.com
www.Iryo.eu
www.Renfe.com

When my mom and I visited Andalucía, we flew to Madrid and took the train to Córdoba on day of arrival. We then took the ALSA Bus to Granada, then the ALSA bus to Sevilla, then the high speed AVE train back to Madrid and ended our trip in Toledo.
We spent the night before our flight home near the airport but we’d visited Madrid on a previous trip.

The main reason for choosing this route was because it worked great logistically. We also chose to travel by bus to/from Granada due to more time options.

Once you decide on the route you want to take, make sure you book your Alhambra tickets soon.

Enjoy your time in beautiful Spain!

For our trip we flew into Madrid and home from Seville. We used ALSA buses and the trains. This was our order, if it helps. (We visited two places not on your list.) I would say the order depends on bus and train schedules.

Madrid
Toledo
Cordoba
Granada
Malaga
Seville

Based on the AVE train I'd go

Madrid
Toledo/Cordoba
Granada
Sevilla
Madrid.

I always arrange my trip so that I'm in Granada on a weekend as the town is so much fun, locals are out dancing in the square, wedding parties. Enjoy your trip, J

We did Madrid, Sevilla, Granada, Córdoba. Chose this route based on holiday during our trip (NYE), and availability of Alhambra tickets.

As others have said, just put Córdoba on the way to/from Madrid, and the rest is flexible.

We did Sevilla - Cordoba- Granada. There are lots of trains to Sevilla, which I think simplifies things if you’re traveling onward after an international flight. More choices on offer. But whatever you do, make sure what yiu want to see is open on the days that you’re going to be any given place.