It is correct French from all points of view, and it means only "I stole a plane.", so there is no problem whatever the context.

If you wanted to say "I flew a plane." you’d say "J’ai piloté un avion.".

There are two verbs that are homonyms and as you said they mean in English, respectively, steal and fly.

But voler meaning fly is an intransitive verb, that is, it cannot be followed by a (so-called) complément d’objet (both direct or indirect).

Piloter un avion, faire partie de son équipage ou être à son bord.

Nous volons vers Rome.

Les avions volent. Un oiseau en train de voler.

Cet aviateur a volé près de deux cents heures.

See

https://fr.wiktionary.org/wiki/voler#Verbe_1

https://www.larousse.fr/dictionnaires/francais/voler/82449

EDIT

The difference in transitivity between English "fly" and French "voler" is not just about that verb. In English, "drive", "ride", "fly", "sail", etc., can all be used simultaneously as a synonym for "go" and a synonym for "pilot". But in French, those verbs are always different. We either say "Je vais au travail." or "Je conduis ma voiture.", but not "Je conduis ma voiture au travail." If you want to convey both informations explicitly: "Je conduis ma voiture pour aller au travail." or "Je me rends au travail en voiture.

merci @Stef:-)!

EDIT 2
See also

Meaning of "J'ai fait voler l'avion"

"Une machine à voler et non à voler". What kind of negation is the "non"?

Quelle est l'origine du mot « voler » ?