This is more of a reference to achieving your dreams. Although Hitler established himself as a dictator and as a result gained a lot of power, the author suggests that he still has a longing and regret for not getting into the art academy. Taking "Billy Bat" back into their own hands is more of a symbolism for having the ability to succeed and conquer your dreams. In this entire manga, "Billy Bat" is viewed as a real thing but I believe that the author is simply using that as a form of symbolism when he wants to make a point. If you have watched the Truman Show, it is like the giant physical barrier that keeps Truman within but actually is symbolism for being trapped in the psyche from all the advertisements, propaganda, and control blinding you from the truth. To clarify, this example is not the symbolism the mangaka is using but the idea behind the type of symbolism he is using.
The only weird part to this is when Chuck says, "If you can do that, then his legacy..." Hitler's legacy isn't exactly peachy and it trails off. Because of this, I am not sure if he was going to say something like "then his legacy would be saved" or "then his legacy would be understood". I believe that this would imply that Hitler's legacy is not actually the atrocities he committed but his ability to follow through on his dreams. However, I cannot confirm this last part.
Let's look at three instances "Billy Bat" is shown in a clear and defined manner (whether in a corporeal form or just a symbol). The first is with Neil Armstrong (Chapter 9: Bat Boy's Great Adventure pages 24 and 25). He is the first person to step on the moon and finds a symbol of "Billy Bat". This is because he had achieved the dreams that he and several other people had and therefore has the "Billy Bat".
The second is with Einstein (Chapters 70: Opposing Billies & 71: Time Travel and Infinite Earths) as he apparently met with "Billy Bat". Einstein was close to achieving his dream as he delved deeper into theories of time and the like but after meeting the "Billy Bat" decides to no longer pursue time travel and admonishes Zofu Sensei for pursuing it instead. Einstein never actually has "Billy Bat" as he did not succeed but because of his potential is able to meet it. Deciding not to complete his dream is most likely because his intellect allows him to see that although with the "Billy Bat" he can achieve his dream, perhaps that isn't the best thing in the long run. It's also where Einstein brings a distinction between the two bats, suggesting that not all dreams are always as great as they seem.
Lastly, we can look at Hitler himself. He uses the "Billy Bat" to realize one of the major dreams he had, but upon achieving it, realizes that perhaps that isn't what he truly wanted. I believe that the whole "destruction of the earth" is more of an idea that stems from the terrible power and evil that can come from the same foundation of what is believed to be good. That is why there are two "Billy Bats" both with an apparently different agenda. I believe that "Chapter 102: Adolf and Hitler" puts a lot of what I am trying to say into context. Sorry for this long answer.
