Which Coins Have The Greatest Growth In The Short Term

My opinion - coins are a hobby and not an investment at least for the vast majority of us. I invest in the US stock market and will certainly have a comfortable retirement someday. Not sure you can say the same about coins.

Most limited release American silver eagles have been highly profitable as a flip, but to get it shipped to you and then flipped you would actually lose the momentum. The flips need to happen asap usually to maximize the profit potential

The usual answer for US coinage, of course, is high-grade branch mint gold, especially Charlotte and Dahlonega (and Carson City, but those don't really exist in high grades).
But I'm not sure if there's any growth still left in those, and I suspect that the vast majority of CCF members - never mind the general public - would have to save up for many years to afford even one of those in the first place.

By "large centers", you mean large cents, right? I did hear that some large cent dates, especially the later ones, are getting more expensive these days.
I don't know much about those; the low grades are common enough regardless (and will probably stay common for a while, aside from the very rare dates/varieties), and the high grades were never within my budget, so I never looked into them.
There's few enough large cents remaining that if collecting them ever becomes popular, the prices would immediately get ridiculous. AFAIK this hasn't happened yet, and if it ever does we probably won't get enough advance warning.

The big short-term percentage option is probably limited issues by the mint: the kind of stuff where you need to be lucky to snap up the coin in the first few minutes, because they get sold out very quickly.
It's not always easy to tell in advance which ones would get the best outcomes in the post-issue market (there's been some that had appreciated by over 10 times...), but if you managed to get at issue price pretty much any limited-mintage coin that quickly sold out, it's almost certainly a good acquisition and you could probably sell it for way more within years.

Past returns are no guarantee of future performance.

My hunch is that by the time anyone can comment on a class of coins that has been appreciating, it will probably have largely run its course, and not be a good investment any more. Same as individual stocks.

I am with those who say coins are a hobby, and the stock market is for investing.
$1000 invested in an S&P index fund ten years ago is worth $2500 today. I am very happy wih that kind of return.
(On the other hand, $1000 invetsed in gold ten years ago is worth less than $1200 today, and silver would be $600).

I do not think there are any coins that have any significant growth in the short term. Because supply is consistent, demand would have to change drastically. A market to increase by a decent percentage would be unnatural and would eventually drop just as fast at some point.

Extreme rarities do not have a lot of potential either. You can get lucky, of course, but it all comes down to buying for the right amount and finding a buyer that will pay a high dollar. I read a book a while ago that was written by an individual that invested millions of dollars in expensive coins, such as an 1804 dollar, and did not have a very good ROI after holding for a while.

Maybe certain mint products can have flipping potential? Even that is risky.