The new fire shelters are a couple of layers of aramid with reflective fabric on the outside. It reflects the radiant heat of a fire, however it can't handle convective (hot air) or conductive (hot object directly on the material) heat.
Like everyone said, it's a last ditch device.
Bringing a tank of oxygen isn't neccessary if you deploy the shelter correctly. If you deploy it incorrectly (not finding a good deployment site or not sealing the edges) then an oxygen tank won't help you because the hot air coming in will burn you anyway.
We don't wear wool, we wear nomex with cotton under shirts, underwear, and cotton or wool socks.
If I didn't have nomex then wool or cotton would be my first choice.
The key to surviving a fire is to not get entrapped in the first place.
I'm glad those guys (and anyone who's been burned over) survived, but the fact that they had to deploy their shelters means something went wrong before the entrapment.
Either they didn't have good escape routes and safety zones planned, they didn't post a lookout, or there was a breakdown in communication.
Firefighting is just like tree work. You scout out dangers, mitigate hazards, and check your safety gear before doing any work.