If built correctly, there are nearly flat roofs that do not leak. School roof that was built back in 69 where I grew up is a good example. But it doesn't "look" perfectly flat, there are ridges and valleys to direct runoff. The problem inevitably starts when you have a spot that has standing water. Over time, with freeze and thaw cycles that standing water will eventually work a hole. So look for any spot that shows up different on the roof. Moss, calcium buildup from evaporating water, missing gravel, etc.
Now here is the exception. Most of them do not have what you discribe.
And often leaks can go undetected for years before they actually make their way to something noticeable.
Runoff isnt the only problem though. Often flat roofs are made using a rubber membrane which is susceptible to damage form all sorts of things including workers being up there.
And its amazing the things that can end up on roofs that can cause damage. Many years ago I worked for a company that used to do all sorts of things on tall buildings from waterproofing to tuck pointing,painting, Steeplejack work, roof repair. etc.
In any event one building we were working on was the Perth Amboy Bank. On that roof we found an entire tree branch. how it got up there or how long it was there is anyones guess. But sure enough it was there.
funny thing about leaks.
Just because the leak is showing up in one spot on the inside. doesnt mean thats where its leaking from on the outside.
Had a customer last year whom I had to replace a ceiling for who had a leak comming through the ceiling on one end of the house.
and the leak on the roof was clear across on the other end of the house.