Gluten free food in carry-on luggage

My son has celiac, too, and I do this all the time and have never had any trouble. Anything non-liquid is fine by TSA. Note that jars of peanut butter, hummus, etc are considered liquid. Once you get to Paris you won't be allowed to bring in meats (so if you bring chicken, eat or toss it before landing), but things like cereal, rice, muffins etc would be fine all the way to Greece.

Also, once you go through security you can buy yogurt or other liquid-y foods and bring on the plane (you just can't bring your own liquids through security but if they are bought at the airport you can bring them aboard.)

I also bring a small bit of GF food for eating there. I stay in apartments and can always find stuff at the local store, but having a little just in case is helpful.

For the trip itself, you will want a card explaining celiac in Greek, so you can hand it to waiters. There's plenty of naturally GF food in Greece, but specifically marketed gluten free food is not common in restaurants.
Note that burgers and meatballs are often thickened with breadcrumbs and flour.

Solid food is fine in the broader sense but may get you subject to secondary screening at security checkpoints because their scanners can have problems telling the difference between a nutrition bar and a block of explosives.

The USDA and Customs are fussy about what kinds of food can be imported into the country over plant and livestock disease concerns, so on the return home, make sure to give anything leftover in the fresh produce/meat product/dairy realm to the flight attendants when they do their final trash sweep before arrival. (Food waste is sent for incineration after it is removed from an inbound international flight)

The difficulty for the airlines in providing a gluten-free meal is that wheat is ubiquitous in standard commercially-produced foods. While rice itself is fine, most rice dishes would include wheat (soy sauce in Asian dishes, or a flour thickener in a curry dish). And most beef or chicken dishes will have a sauce which could well be thickened with flour, even if the meat itself is clean. So for many airlines, the safest and easiest option is fruit and salad.

I once tried ordering "kosher" instead of gluten-free on a British Airways intra-Europe flight in business class. The meals served on the flight was afternoon tea, and at the time the kosher meal offered was a nice salad with lox. Perfect. But by the time our flight came around, the menu was changed, and I was given the standard three tea sandwiches, all meat and veg, no butter or cheese. (The meal doubled as lactose free for those who requested that). And I was not offered milk with my tea. So I won't try that again!

Note that the "gluten free" standard within the EU is very strict. I encountered this on a recent guided hiking trip. The guides explained that they could not always provide gluten-free bread for our daily sandwich buffet, because the regulations require that gluten-free bread must be produced in a dedicated gluten-free facility, not a regular bakery that simply used gluten-free flour. They were not always able to buy the special bread in the tiny villages where we stopped for the night.

You should be OK in the cities in Greece, but you might want to carry some gluten-free baked goods along with you if you are visiting small villages.

I'm not GF but I am vegan so I always take some food with me for the flights.

The last time I flew (last May) TSA had bumped up secondary screening on food in carry ons. Going thru security at my small airport the lady ahead of me and I got bumped to the secondary screener. She had cookies in a Tupperware container (Grandma going to visit grand kids, lol!) and I had stopped at the grocery store on the way to the airport and purchased a sleeve of bagels. The screener ran the explosives testing stuff over her container and on the outside of my bagel wrapper altho they didn't look at the foil packs of nut butter I had in my 3-1-1 liquids container.

Other than liquids, there is no problem taking food thru US security. As mentioned, meat and fresh veggies/fruit can be an issue in your arrival country when you go thru customs but if you just taking enough to last you for the flights then you'll be fine.

Give yourselves extra time at security (for me-small airport, I allow 10 minutes. For a big, busy airport I might allow 20-30 extra minutes in case the food triggers a closer inspection.)

PS While I appreciate the effort of airlines to provide vegan food, in general it is awful. They seem to think that everyone that is vegan is from a curry-based cuisine. The curry hot-pocket for the "Breakfast" snack on Delta (which has been served for years) is just unbelievably bad.

Pam, next time say you are vegan AND gluten-free, and you won’t get that awful hot pocket thing.

I am always 'favourably' pleased with the amount of GF I can find on my travels. I do carry meal replacement bars and some granola bars (as I am not celiac) and have not had problems regardless of the international flights. My one intermittent issue is the meal replacement bars. They are sort of fudgy - which means visual checking as it seems fudge looks like C4 explosive on the scanner. So I just keep those it either a separate bag handy for removal or in an outside luggage pocket.
As to food on a plane, I used to buy it in the airport, but last week took a dressed salad from home through security. I see other people traveling with home made meals on planes as well.
I find some Googling can help. If you don't already know it, HappyCow dot net is a vegan restaurant/grocery store finder on a global scale, but also covers health food stores and GF foods. I can then go to the store website (often in English) to see what sort of things it carries.
I also find blogs about GF or Celiac travelers to ???country.

Hopefully you are doing a short apartment let or someplace with a kitchen to ease the stress of finding food.

I was just reading about bringing on foods to flights, and while not specifically about gluten-free foods, this article had some creative suggestions:

https://www.tripsavvy.com/taking-food-on-a-flight-2972600

Did you go yet? If so, any places to recommend that are safe?