Empirical Answer Considered!
(see the end of the question for details)
Iridium satellite flares are a class of Satellite Flares that originate from satellites in the current Iridium constellation. Unfortunately, according to this helpful answer and as foretold by this one (though schedules have slipped) they are going away relatively soon.
Reflections come from fairly flat antenna panels on the satellites. The attitude of the spacecraft and especially the antennas are carefully controlled, and so the path of the footprint of the reflected light can be predicted with surprisingly good precision.
The web site Heavens Above will give you predicted visible flares if you give it your specific location. It estimates the brightness based on the your position relative to the position of the maximum brightness point of the flare. You can see it if you are tens of kilometers away, but it will be maximum if you are within only kilometers. Heavens Above has been around quite a while and I believe there are other prediction sites and services.
There will be an ephemeris for the position of the sun, satellite, Earth, and the topographic location that you specify.
There will also be an ephemeris or algorithm that handles the attitude of the spacecraft and/or the orientation of the antenna panels themselves.
There has to be some kind of model for the shape of the illumination footprint from the panel in order for the prediction to estimate the brightness based on distance from the maximum.
Is there anything written about this? Is it just a fuzzy blob based on empirical or anecdotal reports, built up over time the way meteor counters build up data used to model debris trails in space? Or did someone actually take a specimen of an antenna panel outdoors and just do the experiment - hold it at different angles wrt the sun and an observer, and measure the brightness?
What goes into an Iridium Flare prediction model besides the ephemerides?
below "View of one of the Main Mission Antenna. The hinged base is on the right side." Cropped. From here.
below cropped (and enlarged) image of a first generation Iridium satellite, showing a bumpy and diffusely reflecting metal antenna panel of the type responsible for producing the flares seen on Earth. From here.
Empirical Answer Considered:
One could conceivably just query a flare simulator a bunch of times, stepping by 1 or 2 km along an East-West line to build up a plot of the cross-track brightness as a function of lateral distance from the track.
Curious if it is different for each satellite, or each of the antenna panels, or depends on sun angle, or if its just a fixed width and the same every time.
A good one of those would definitely be worth