I think it is very likely a parachute. It moves in a swinging relation to the heat source because the heat source is hanging from it. It doesn’t exhibit reflection across the center of frame like you’d expect from a lens flare, and you can see frames in the video when the partially IR-translucent parachute overlaps itself showing that it’s a physical material moving around and which IR light can partially pass through.
It is black hot. We know this for sure because someone in the DoD previously leaked a single screenshot of the video, which did not have the on-screen data elements redacted, and you can see the BLK indicator. That person believed the star shape was the physical shape of the object, not a lens artifact, and told this to the UFO influencer they leaked it to. That’s how this particular video eventually ended up included in this data dump.
The smoke trail must cool rapidly and be colder in temperature than the flare itself and the parachute above it. The ambient air temp and time of day may be relevant to this (direct sun could contribute to warming the parachute). Since it is infrared footage, the colors are all based on a dynamic range, so the smoke only needs to be slightly colder than the parachute in order to appear lighter in color.