Parachutes don't repeat their motions exactly. This here is a caustic reflection and it does when the object re-assumes the same relative position.

Military aircraft IR systems don't have lenses, so there is no lens flare. The bloom pattern of the "star object" also tells you as much. That's an IR laser aimed at the FLIR pod.

When you concur this is BH, the trail being white means it is below the detection range. That's usually -60°C for the sky. When that trail "cools rapidly", that would mean it had to radiate strongly, which would obviously be visible here. It's also very unusual for such a "smoke trail" to cool below ambient temperatures (that sky, which isn't white).

That trail also obviously tracks the movement of the object. Which should tell you, it cannot possibly be "a flare". The most likely explanation is an infra-red laser aimed at the FLIR pod, screening the actual vehicle responsible.