The flames don't actually disappear even though they are visible in the preview but not in the actual photo. After messing around in replay photo mode, I started to realize that the position of the vehicle changes when you activate the shutter. In other words, the car moves slightly backwards from the photo preview when you activate the shutter, causing it to cover up the flames (this only applies to photos in which the car has a forward motion in the first place). Pretty easy to see for yourself: Enter photo mode from a replay and position the camera so you're looking at the side of the car, then move the camera very close to the front or rear bumper (still looking sideways) and make a mental note of the distance between the edge of the bumper and some object in the distance. Set the shutter speed to 1/8000 for minimal blur and press the shutter. In the final photo, the distance between the bumper and whatever object you used as a reference will have changed, meaning the position of the car changed.
I'm guessing this is due to the bizarre way in which PD programmed replay data. The same thing that causes downloaded replays to have funky engine sounds and likely the same reason we haven't had fast forward or rewind functions until recently (also the cause for the half-arsed rewind/fast forward). Most likely, PD tried to code the game to have better graphics in replays and in order to free up system resources, they had to compress certain parts of the replay data such as vehicle position, timing, etc.