When we found the (probable) military compound at 11.388655° 43.139259° I thought it was likely part of the explanation and sort of lost a bit of interest.
Some troops from there had moved a short distance to the east and fired something approx. ENE. Where we can first see the object would have been very close to the point on the ground from where it had been launched/ fired.
But the object appears to cross (very,
very roughly) approx. 2.5 km in the horizontal plane in something less than 2 seconds.
If it were something fired from the ground, the shortest path it could take would be a straight(ish) line essentially parallel to the ground, minimum speed would be in the region of 1250 m/s. That's 4500 kph, 2796 mph, Mach 3.673.
If there were a significant upward element to the flightpath, the distance covered would be greater and speed would have to be higher.
The Djibouti army probably doesn't have anything that could reach this speed (Wikipedia
https://en.wikipedia.org/wiki/List_of_equipment_of_the_Djiboutian_Army)
Contemporary tank cannon can have muzzle velocities in the 1600 - 1750 m/s range, but projectile velocity drops during flight* and Djibouti doesn't have tanks.
Maybe the cannon of its (three) WMA301 vehicles are in the 1400-1500 m/s region but again velocity would drop in flight (and they might be lower-pressure, lower velocity variants of the gun they were derived from- if not, these
might be the only halfway plausible Djiboutian candidates).
The Djibouti army's artillery have lower muzzle velocities; D-30 guns around 700 m/s, M109L SPGs maybe approx. 810 m/s (Rheinmetal, 155mm Modular Charge System,
https://www.rheinmetall.com/Rheinmetall Group/brochure-download/Weapon-Ammmunition/B284e0920-155mm-artillery-modular-charge-system.pdf).
Some surface-to-air missiles can reach/ exceed the mystery object's speed; most US Patriot missiles 1190 m/s, a recent variant 1887 m's in a test; Soviet/ Russian SA-300 and successors 2000 m/s and higher. But these are large systems, and Djibouti doesn't possess anything like this.
Smaller man-portable SAMs are slower (FIM-92 Stinger approx. Mach 2.2; Shorts Starstreak might be the fastest, >Mach 3); not fast enough for our mystery object (and none known in Djiboutian service).
I now think the presence of the military compound is a coincidence (though maybe it had something to do with there being a US aircraft monitoring the area). Back to considering a small object much closer to the camera.
*I can't tell by eye whether the object's apparent speed changes or not, does anyone know?