I read about that car accident the other day. Tragic. However, these products, like the Draeger or Safe Escape, are smoke hoods, and not intended to withstand direct flames for any length of time. There's also a good chance that if the surrounding air is hot enough to burn you severely, the air from the filter may also be hot enough to burn your lungs. The filters on these smoke hoods do not have any capacity to significantly cool incoming air.

This is probably something that may freak out someone who actually has to use a smoke hood in a fire. They may think that putting on a hood should somehow provide cool, clean air to breathe but it turns out to be hot, too. ParamedicPete mentioned staying out of oxygen deprived areas because they don't carry any oxygen on board. You also need to stay out of areas that are too hot when using these smoke hoods.

For the scenario you described, a big extinguisher might be more useful in buying some precious seconds to extricate a trapped child rather than going into the flames with just a flame-resistant hood on, to say the least of the rest of your unprotected body, like your hands/arms.