The short answer is no, it’s unlikely that the flares could be predicted however the reason for this answer deserves a more detailed explanation.
To an observer on the ground a satellite appears to flare due to the fact that a certain part of the satellite is reflecting an image of the sun down on to a particular spot on the earth. If it is a large, flat, highly reflective panel (such as the main mission antennae (MMA) on Iridium satellites) then the reflected image of the sun’s disk is well constrained into a relatively small area (typically a few 10s of km across) and the flare has the potential to be very bright. If however the reflective surface is not flat then the reflected light is scattered into a wider area and hence the flare will not be as bright.
As the earth orbits the sun and rotates on its axis, and the satellite moves in its orbit around the earth, the relative positions of the sun and satellite change and the position of the spot of reflected sunlight moves across the face of the earth. An observer on the ground therefore sees the flare if they happen to be on the track of the reflected spot of light as it moves across the face of the earth.
If we know the date, time, observer’s position on the surface of the earth and position of the satellite then we have enough information to determine if the satellite is above the observer’s local horizon (while the observer is in darkness) and the satellite is in sunlight – this is the basis for all predictions of satellite visibility.
In order to determine if a flare will occur we need to know some additional information, specifically:
1. The satellite’s shape / structure (does it have a large, relatively flat shiny panel?)
2. If such a panel exists, is the satellite’s attitude in orbit maintained in such a way that the orientation of the panel can be reliably predicted.
In the case of Iridium flares, the answers to 1 and 2 are both “Yes”. Each Iridium satellite has three MMAs (large, flat, shiny panels that are located at 120 degree intervals around the main satellite bus, tilted out at a specific angle) and the satellite’s attitude with respect to the surface of the earth and it’s orbital trajectory are maintained with a high degree of precision: the main satellite bus is orientated vertically with respect to the surface of the earth and one of the MMAs always faces into the direction of flight.
The problem we have with military satellites is that we do not know much about 1 and 2 as this information is typically classified. The fact that you’ve seen flares suggests that there is a reasonably flat shiny panel on the satellites. Is this a solar panel, an optical sensor, a communications dish or a RADAR antenna? We don’t know – and even if we did, are the positions of these predictable (and in the public domain) in advance? No, I’m afraid they are not.
Another complication is that the orbital elements of military satellites are not always very precise. For the Chinese Yaogan satellites, the US Military does helpfully make these publicly available (typically updated twice per day based RADAR returns) however they do not do the same for their own military satellites. The orbital elements for these are derived by the amateur community from visual observations and while reasonably accurate, an error of a few seconds could lead to a large uncertainty in flare visibility for a given position on the surface of the earth.
Given enough observations it may be possible to build a model that could be tested and refined. This is what actually occurred with Iridium Flares – the flares were not predicted in advance – it was by noting that flares were occasionally seen and by reviewing publicly available information (regarding the satellite’s structure and attitude maintenance) that a model was built, tested and proven to be accurate.
On a final note, the current Iridium satellite fleet is approaching the end of its operational life and they are being replaced by next generation models which do not share the same design MMAs of the current satellites. In time the older satellites will be decommissioned and their attitude will no longer by maintained. Hence the ability to accurately predict Iridium Flares will decrease. Enjoy them while you can!