Black Kites are widespread throughout Eurasia, Africa, and Australia. Some populations are migratory and some are resident. In Australia, Black Kites are largely nomadic and probably move around a lot in response to seasonal changes and other challenges/opportunities macdoc describes.
These birds are commensal with humans in many circumstances, feeding from garbage dumps, slaughterhouses, scavenging roadkill, etc. They also take fish, amphibians, small mammals, insects, etc. They are an ultimate human-associated generalist.
During the breeding season, individual birds by necessity become quite sedentary, in addition to the several weeks (~20 days?)they must spend jostling for territories, building nests, etc., the nesting birds are tied to their breeding home range area. Once the eggs are laid, incubation will take another 35 days or so, fledging will take an additional 45 days, and the young birds are not likely to be independent for another 30 days thereafter. So that's a rough estimate of 20 + 35 + 45 + 30 = 130 days at a minimum that the birds are not just free to wander wherever they see smoke on the horizon.
In Australia, nesting occurs during Jul–Nov (dry season). This is described as highly variable, but I assume that birds nesting in Jabiru, for example, would start in July so the young are independent before the worst of the rainy season sets in. Perhaps where the monsoon is not so extreme they get started a little later, but I don't know.
So...during the height of the dry season (when the fires are burning, right?) those birds cannot access fires that aren't in proximity to their individual home ranges. They can wander around chasing smoke December–May, but I don't expect much burning happening then as it's the wet season. As it gets dry enough to burn in May and June, that's when the birds don't have the freedom to chase any far away fires.
THIS is what I mean when I assert that each individual bird does not have many opportunities to forage along fire fronts over the course of a year. It might be just a few days within the foraging range during their sedentary nesting period and really unpredictable during the rest of the year when the birds are more mobile but conditions are less conducive to fire.
Australian friends, I'd appreciate your feedback on whether this makes any sense.
Source life history info on Black Kite.