the rm file has audio, but it's shot from some distance away. So you do hear jet noises, but it's not distinct. There are 5 other F16Cs flying around and 85,000 people around the cameradude, so it's hard to say.
The first of the still pictures in the series says it's shot 4 seconds before impact, and shows what looks like full burner.
The next one shows the seat burning, the canopy in the air and heat distortion from the exhaust of the jet, but no burner.
I saw no news stories mentioning a flameout.