What's the difference between flat, matte, and gloss?

Matt is "not-shiny". Gloss is "shiny". In-between is "semi-Matt", or "semi-Gloss".
Which one of these an aircraft finish should be depends on when and where the aircraft was being used. Most WW2 aircraft camouflage schemes should be matt or semi-Matt, for instance. There's no one answer; you will need to do some research (or ask some specific questions).
Bruce Melbourne, Australia

Yup...matte also doubles as "semi-gloss" in some circles...

Take trip to your local hardware store, visit their paint department...many suppliers provide visual aides to help understand the differences between each.
Flat=absorbs light Gloss=reflects light
Another way is to look at different photo paper finishes to see the differing effects translates.

Matte & flat are both dull. Same thing. Gloss is shiny, semi gloss or semi matte/flat are in between.

This is not quite the full story. White reflects lots of light, black doesn't.
Glossy means shiny. A mirror is the best example of perfect gloss. In a glossy paint job you can see reflections. You may even be able to see yourself in a glossy black finish.
A matt or flat finish may reflect lots of light, or little, depending on its color. But the light it does reflect goes scattered off in all directions. You cannot see your reflection in a matt surface, even a matt white one, which reflects 95% or more of the light, but is not a specular or shiny or mirror-like reflection.
Look at a black finished car. If it is polished the body will be a glossy finish. Now look at the tires. They will be matt black, unlike the glossy body. You can see yourself reflected in the body, but not in the tires.

Thank you, everybody, for your assistance. This answers my question.

Howdy,
This site equates matte and flat and from what I've learned, they're about the same.
A flat finish is great for hiding imperfections and it also defuses the reflected light. This is why it's used on ceilings and most of your walls. Folks get into semi-gloss, eggshell, etc., where there is high usage, fingerprints, a need to wash, etc. You use this type of paint in the kitchen and bath. However, if you notice - the glossier it gets, the more imperfections in the plaster are noticed. It also reflects light in a more harsh and glarish (is there such a word?) way.
However, many models, particularly military look best when finished in flat or matte.
In coins, there is such a thing as a matte proof. It's a flat finish. This is in contrast to most modern proofs which are extremely polished and mirrorlike. Where they get very lovely, is when they are a Cameo Proof. This is where all the raised portions are frosty in a flat or matte type finish and the background is mirror like reflective. These are very popular.
just musing,
rono