Well, the Empire of Japan never had a separate Air Force branch during the Greater East Asia War, so it is somewhat understandable.
They do have the Army Air Force during WWII. That's where their Hiens, Hayates and Hayabusa (aka Army Zero) are attached to.
Even though Yoshika's supposed to be the Naval Air Arm, she's not operation out of or attached to any naval fleet during the Gallian Neuroi campaign. Well, not like any other member of the 501st is attached to any naval air arm in the first place.
Update: Ah, I see. Thanks for the reminder, zgryphon. It's been a while since I last watched Strike Witches and some details have skipped my mind.
Well, not like any other member of the 501st is attached to any naval air arm in the first place.
According to the first series artbook, Yoshika and Mio are both technically members of the Imperial Fusō Naval Air Service's 24th Carrier Division, 288th Flying Corps. What ship they're associated with is not specified, but in the first series it's probably Akagi. Shizuka in the movie is also an Imperial Navy pilot, though she's not actually a member of the 501st JFW.
(There are witches from the Liberion Navy and Marine Corps in other World Witches branches, but not in Strike Witches.)
They do have the Army Air Force during WWII. That's where their Hiens, Hayates and Hayabusa (aka Army Zero) are attached to.
Yes they did have an air wing for the army, but in either case that they never had a dedicated branch much like that of the German Luftwaffe, British Royal Air Force, or French Armée de l'air she would still be wearing the wrong uniform which is more based off of the post war reorganised American standard than Imperial Japanese.