"Incinerated" may be a slightly strong word, but "fatally injured by burns" is entirely accurate. Most of the fatal and life-altering burns suffered in Hiroshima and Nagasaki were effectively extreme sunburn. Most of the burns victims were burnt only on one side of their body - the side facing towards the blast. It doesn't take a lot of material to protect you from that flash. Many people suffered burns only to their face and hands, while the parts of their body covered by clothing was uninjured. Some people had the pattern of their clothing burned into their skin; the darker colors of the pattern acted as a photomask. Eye injuries were very common, because many people heard the bombers flying overhead and went out to look.
I am aware of this, which is why I said it could protect you from surface burns. The parent didn't just say "incinerated" - it said "completely incinerated". I don't think there's any scenario involving "complete incineration" where a blanket will help.
The thermal radiation pulse is very short, on the order of seconds and it may arrive faster than the air blast. If you are close enough to the blast for your blanket to be vaporized and moved away from your body that quickly, you are likely being concurrently killed by the fireball, ionizing radiation, and overpressure.
Something that was recommended in UK civil defence material from the Cold War was painting windows white - this sounds silly (and was often derided) but is actually a pretty good mechanism for keeping thermal radiation out of the inside of buildings.
Of course the outside would still be on fire. Most of the UK has either wooden or plastic window frames.
The absolute best outcome would be lower burn rates in the outer rings of the heat zone.
But in a full exchange fallout levels would kill those people regardless, and even if fallout didn't, they'd still starve.
I've seen maps from the 1950s - before the huge warhead build-up - which showed most of the UK being reduced to desert by fallout.
In reality, in a full exchange the larger cities would be hit multiple times, so the short-term odds of survival for anyone within 10-15 miles of a large city would be essentially zero.
I don't think this can be right. Surely it takes far less energy to vaporise a blanket than a whole person.
It might protect you from surface burns caused by the infrared pulse, though. And flying shards of glass.