It is normal but not essential to repair a leaking flat roof using the same materials as those originally used. However if your flat roof is an old lead or zinc roof, and isn't visible from the ground, using the same materials for the repair is an unnecessary expense.
In this case we would normally repair it by patching the leak using "torch on felt" or "liquid rubber" rechniques. Both these processes will last between 10 and 20 years, and if it's an old flat roof they'll probably outlive the roof itself.