Oda's work is unique like that for some reason, like Cracker was shown first in Big mom's crew, Ace for Whitebeard's, Burgess for Blackbeard, and Ben Beckman for Shanks.
There wasn't a particular order when revealing who's who when it came to rankings. I thought that it's only First Mates that have a billion bounty based on Dogtooth?
Only none of those are comparable. Context is rather important here as Ace was introduced as Luffy's brother that happens to be a WB commander, not as a means to introduce the WB crew. That would only become relevant during the Marineford arc. The BB crew was introduced almost simultaneously and in a rather random fashion. I think no one expected them to become what they are now and Shanks' crew on the other hand did got introduced simultaneously in the very first chapter.
More importantly though none of these were crews that the Strawhats had to face in the near future, not even the BB crew. After all there's no immediate reason to introduce a group of characters over a certain duration of time based on their strength when that's not relevant for the ongoing plot.
Also there are very well multiple instances Oda did introduce the strongest character as last. More recent example: Dogtooth. From a story perspective this also makes sense as you can build up suspense. Assuming that Jack would be the strongest Calamity, that would be rather underwhelming. Despite that I liked the way how he has been portrayed, that doesn't change the fact he wasn't able to overcome the Minks till he used Caesar's gas and got one-shotted by Zunisha. I'm not saying that therefore he's weak or something, but if you take into consideration that he was the first introduced 1B bounty and he's supposed to be Kaidou's strongest subordinate...well yeah that feels really anticlimactic. It would simply be much more beneficial for the story for Jack not to be Kaidou's strongest soldier.
On the other hand it's unlikely that Kaidou has three subordinates with bounties of 1B and higher, while BM has only one. Their crews are supposed to be near perfectly balanced, however when the bounties are that high, it's rather unrealistic to think the amount is going to be exactly the same. A difference of 50m makes little difference.
So the most logical conclusion that can drawn from this, is that Jack is the 2nd strongest of the Three Calamities. That his bounty is exactly 1B also can support this as it's the lowest bounty you can have with 1B threshold.
A note in Oda's office said "Kaido, King, Queen, Jack." That's pretty definitive proof that they're names/nicknames are King and Queen imo. Oda clearly planned to name them King and Queen at one point in time, and since every other important Beast Pirate has been named after cards, I doubt that Oda's changed his mind.
I know, I have seen the picture, only to me it wasn't that particularly clear and you can't disclose the possibility someone intentionally altering it. It's also possible that it are temporary work titles and/or that he changes his mind. There are other characters that have card-related names that are not part of Kaidou's crew and other characters that are, but do not have such names.
So no this is not "definitive proof". Definitive would be that they, or at least one, are actually introduced like that in the series. This is, as I said in my OP, enough to have a strong basis, but not that it's already proven. In particular because Oda doesn't always literally take over specific terms or names, but makes puns on or adaptations from them.
The Calamities will have higher bounties than their SC counterparts because they're much more evil and commit crimes more frequently. The fact that Jack has a bounty lower than BM's #1 makes it nearly impossible for him to be Kaido's #1 since if he was on Katakuri's level, his bounty would be higher than Kata's because Jack loves to kill people, unlike Katakuri.
That's completely baseless. You have absolutely no idea what all the Sweet Commanders and Calamities have done in the past. In particular because you don't even know two of the three Calamities. You are solely basing this on the fact that Jack is seemingly more brutal and less understanding than Dogtooth, but that is not something that automatically reflects in their bounty. In the end all of them are still the subordinates of two highly erratic and cruel Yonkou.
You know im a believer of the jack queen king, but... If big mom has the strongest family... And katakuris bounty is only a little higher than jacks, than i don't see how theres a queen king without their bounty being higher than katakuris, which they shouldnt be if big mom has the stronger crew... So maybe jack is the first commander
Their crews are balanced. As I said previously it's kind of unrealistic to expect that they will have the exact same bounties, but when they are that high, having differences of around 50m makes little difference to be honest. Likewise Jack's bounty is also only a little higher than Smoothie's, who is the 2nd strongest of the BM crew after Dogtooth.
Not to mention Sabo who is the chief of staff in the revolutionary army rebellion only has a bounty of 602 million that is equivalent to the former 4th commander on Big mom’s ship, Snack.
Dragon on the other hand is the most wanted man in the world.
Sabo is part of the RA, which is a completely different entity than the Yonkou. They are organized and operate differently and really can't be compared to how the Yonkou do things. Not to mention Sabo is 22, which is far younger than all the Sweet Commanders and most likely the Calamities too. For instance Cracker is 45, Smoothie 35 and Dogtooth 48.