Sky Captain and The World of Tomorrow/WMG

Dex is Totenkopf's son.
Not an epileptic tree so much as a small sprout with poor coordination. The only two people in the world who can create Raygun Gothic wondertech? One old enough to be the other's father? It's not only a no-brainer, it's a negative-brainer.

Totenkopf and Dex are Sparks.
Again, not exactly Atomic Rocket science, here.

The dinosaurs and monsters on the island weren't created by Totenkopf's experiments. Totenkopf was created by their experiments.
A race of superintelligent beings needed a human representative to deal with the outside world, so they made a creature with a human appearance but their level of intelligence; but the prototype was flawed with a psychotic imbalance, and overthrew their society, driving most of them out into the wilderness, but creating an escape rocket to save his followers. Dex was a more successful product of the same project, but escaped to find human allies that he could maneuver into attacking Totenkopf.

The movie takes place in the same Alternate History as The Rocketeer.
Think about it: Airships still cross the skies, weird science like the one that created the rocket pack is not unheard of (and even goes further) and the 1930s are still in full swing. It wouldn't be a surprise if Howard Hughes lent Dex a hand in customizing Sky Captain's planes. Though any US plans to start a war with Nazi Germany, especially in light of the Los Angeles incident, would have taken a backseat following Totenkopf's attacks.
 * I dig this theory. Though I think it would be more accurate to say The Rocketeer was an unofficial prequel to Sky Captain, since it happens before America entered the war, Sky Captain seems to take place after such a war happened, and there isn't as much rampant retrofuture tech around. Perhaps the notoriety that The Rocketeer garnered led to the formation of mercenary groups such as Sky Captain's private military with advanced technology as opposed to government-funded military, which led to a Weird War II that ended sooner than in our reality.