@C.C. 95 @mllNY @Wreck
It can indeed take a few months to get some of these screenprints to be perfectly flat so the issues your experiencing with them not going flat in a couple weeks simply is a matter of time. Even then some of them simply never want to become perfectly flat. Its just the type of paper that some of these are printed on that cause this issue and no matter what you do there are a stubborn few that want to slightly curl at the edges. But most will get perfectly flat its just a matter of patience.
One thing I will suggest that sometimes helps with flattening prints (again requires more patience) is to let the prints "breathe" when you take them out of the tube before putting weights on them right away to try and force them to flatten. The fibers within the paper, if you let them just relax and take in some oxygen on there own after taking them out of the tube will let you flatten the print easier when you put the weights on them then just say putting weights down on the print right away. What I mean by letting the print breathe is simply to just let the print sit there curled how it will naturally after you take it out of the tube. Leave it there for as long as you can... I usually do 3 - 5 days depending on the print sometimes even a week. Then I put it into my foamcoare sandwich and into a drawer in my flat file to safely flatten and I forget about it for 2 - 3 weeks, usually flip it at that time over and forget about it for another 2 -3 weeks.
Of course I take my time and Im sure you can speed this up with heavier weights and what not but Im usually in no rush.
Hope that helps.