It’s getting cold where I live and I sleep with multiple blankets. I am wondering whether it generally matters how I might use blankets to keep something warm; if I put blanket $A$ on top of blanket $B$, will it better insulate something than if I had put blanket $B$ on top of blanket $A$?
Such a system is actually quite complex, and as any backpacker would know, what keeps you warm is the amount of dead air within the layers. Dead air is non-circulating air. If we ignore the dead air between the layers and only consider the blankets themselves, I would say it's the same. However once you consider dead air and other parameters as in reality, the order does matter.
A small plus :
My personal experience as well as my friends, the best setup for different sleeping bags is to have the low temperature ( warmer ) sleeping bag outside, and the high temperature ( colder ) sleeping bag as a liner.
each blanket layer represents a resistance to the conduction of heat. the heat flow resistance of a stack of blankets is then the sum of the resistances of each individual layer within the stack because to flow all the way through the entire stack, a parcel of heat must traverse each layer in it.
The ordering of that sum does not affect the value of the sum, and so the ordering of the blankets will not affect the total insulating capacity of the stack.
If this were true, then you could build a blanket exhibiting two different warmth levels depending on which way you flipped it. You could then use that blanket to divide a box into two halves in such a manner that heat would flow more readily into one side of the box than the other- in essence, making a "Maxwell's Demon blanket".
This discussion pertains ONLY to conduction; a different treatment is required to deal with radiative transfer.