And, as Narius implied, it's an activation requirement -- not a resolution requirement.
So, after you've activated the 2 "Accumulated Fortune", you can add other duplicate cards/effects if you wish. For example, this is a legal chain (assume you have 5 Set S/T cards):
Chain Link 1: Your opponent's "Heavy Storm".
Chain Link 2: Your "Jar of Greed".
Chain Link 3: Your "Chain Detonation".
Chain Link 4: Your "Accumulated Fortune"
Chain Link 5: Your "Accumulated Fortune" (because at the time you activate it, there are no duplicate cards/effects on the chain).
Chain Link 6: Your "Jar of Greed".
Now, you would no longer be able to activate any "Accumulated Fortune" (or other cards with the same activation requirement), since there are now multiple cards with the same name on the chain. However, another "Jar of Greed" or "Chain Detonation" is fine, because having duplicate cards/effects on the chain during resolution doesn't affect AF's ability to resolve properly.
Also, as Narius pointed out, you posted this in the Single Card Discussion. Please remember to post rulings questions in the TCG Q & A section in the future (I'll move this one for you; future ones will be locked or deleted). Thanks!