I have been curious myself about the flammability of carbon fiber, and the first result on Google (for me) is the FAA report Flammability Properties of Aircraft Carbon-Fiber Structural Composite. The report is quite technical and doesn't list direct implications for its use in aircraft, probably intentionally since only small samples were used in the tests, and I'm not going to speculate on what happened in this incident. But a few notable takeaways from the report that I interpret (as someone who is not an expert but is somewhat familiar with this field) are:

- Aircraft (and almost everything made of "carbon fiber") are not made of 100% carbon fiber. The material used in the tests is 60% by volume carbon fiber (which is typical) with the remainder some type of plastic resin which binds the carbon fibers together, hence the common name Carbon Fiber Reinforced Plastic or CFRP. It is this plastic resin that vaporizes and burns, not the carbon fibers themselves, which do not burn easily and need much higher temperatures.

- Under their test conditions, CFRP remains structurally and chemically intact until it reaches about 300 °C. In the range of 300-500 °C, the plastic resin decomposes and escapes, and then burns, which leads to the swelling as gases escape. Above 500-600 °C the resin is more or less completely decomposed, and some charring of the carbon fiber occurs, but not bulk burning of the material. For reference, aluminum melts at 660 °C although the actually alloys used will vary.

- Carbon fiber is quite a good heat insulator. It tends to take relatively long to ignite, and after the surface resin burns and vaporizes, the carbon fibers remaining insulate the surface, slowing down decomposition and burning in interior layers of the material.

- The material does not support combustion by itself, it will smolder and the flame will die out unless the flame gets to a high temperature. A relatively large amount of external heat is needed for continued decomposition and combustion. The amount of external heat is the main variable in determining how fast CFRP decomposes.

- The burning process can look different and spread differently than most things burning because CFRP is made up of layers which have specific orientations. The final result of combustion ends up being thicker than the initial material due to layers spreading apart, but the resulting material consists of mostly carbon fibers which are black or dark grey. It also is very weak, since nothing is holding the fibers together.

- A relatively high amount of incomplete combustion products are formed, namely soot and carbon monoxide, but if flames are present the carbon monoxide can then be converted to carbon dioxide.

When talking about flammability, it's not a yes/no question that needs to be answered. It is of course more complicated, and a better way of thinking about it would be 'how are the hazards different than an aluminum aircraft'?