Iridium satellite constellation consists of 72 satellites, 6 of those on-orbit spares, and since May 1997 to June 2002, in total of 95 Iridium satellites were launched to orbit. Wikipedia currently lists 17 defunct Iridium satellites. Two of them decayed, Iridium 33 collided with Kosmos 2251, 6 in uncontrolled orbit, one presumed partially operational, and additional 6 in their nominal orbit. That list seems a bit outdated though, and searching through NORAD catalog, at the time of writing this answer, I managed to find only 70 Iridium satellites that aren't tracked as debris and haven't yet decayed.
All that means that not all of their orbits will have identical orbital period, i.e. some will be in slightly higher orbits than others. Operator might have also moved some of the on-orbit spares to closely matching (trailing or leading) orbits to some of by now defunct satellites to ensure global coverage. So the Iridium satellites, defunct on-orbit ones and active ones, can appear to converge over a small area of the sky as observed from a location on Earth, and would produce a flare at a specific angle to the observer at nearly the same time, due to same or similar orbital geometry, small angular separation as observed from the ground, and reflecting light from the same distant source.
How close can they get? Well, theoretically, angular separation between two Iridium satellites as observed from the ground can be 0. So, really close.
Mind that not only Iridium satellites produce satellite flares, and there's a lot of junk up there, from tumbling upper stages, to other defunct satellites, many of them in similar orbital inclinations, so chances that two or more of such object produce a flare close to each other increases. For example, just at this exact moment, there's this many object in orbit over the area I live at and directly overhead (there's many more at shallower angle to the horizon):
Objects in orbit currently appearing directly overhead to an observer in central Europe. Made with SatFlare