In Canada we don't use Fire Shelters, because they are too dangerous. Very popular in the USA though.

It's important to understand the three types of 'fire energy' (or exothermic reaction) to best explain an answer to your question. Fire travels three ways: Conduction (direct contact, like a stove cooktop element), Convection (non-direct contact, like a toaster oven) and Radiation (non direct transfer of heat).

A fire shelter like youve described, a fire blanket, would at best provide resistant shielding against conduction (the fire couldnt touch you) and convection (the fire couldnt heat up air that would touch you). However, you'd be cooked nice and good just by radiation alone.

As an example, In BC Canada, we have serious forest fire problems. In Kelowna a few years back, fire was spreading from home to home via the radiant energy from the fire in one home igniting curtians in another. An example of the reality of fire radiation potential.

TL;DR: don't ever expect a fire shelter to save your life, because it is already responsible for taking the lives of far too many firemen.