As I tell people, if you want a GOOD movie written in a stylized 1938, watch Rocketeer. They took the pulp magazines and did it right.
The opening scene always gives me goosebumps, since the first thing is a James Horner score piece as a GeeBee racing plane is rolled out of a hangar at dawn, prepped, cleared, and started, with that massive Wasp radial whining, coughing, then roaring into song from a close camera angle, with amazing Surround. Also, in widescreen, a Zeppelin coming in over Griffith Park Observatory is a complete "Okay. That's...really big" moment.
It's also got all the correct story elements. Gangsters, G-men, Nazis, a secret jet pack, a Valentino-like movie star, a brash pilot, Howard Hughes, an autogyro, a Zeppelin, and an extremely attractive, younger Jennifer Connelly.
Side note, the soundtrack includes two excellent period songs newly recorded, "Begin The Beguine" and "When Your Lover Has Gone", from the scenes in the formal dinner club.
There's also an animated B&W Nazi propaganda film in it that's shockingly close to the animation style of the real thing, showing how the "rocketmen" will spread across Europe and the Atlantic and bring the Reich, shown in its entirety.