] Does anyone know what ‘Napoleon blankets’ are?

No: you've stumped me on that one -- and googling shows up nothing. It's an odd phrase, for one thing: the British tended to refer to the man as Bonaparte rather than Napoeleon during that period (ie they acknowledged that he was a general, but not an Emperor and entitled to be referred to by his Christian name). Googling shows up nothing on Bonaparte blankets, either.

] Was this the hysteria-driven Regency equivalent of plastic sheeting and duct tape?

There was a serious possibility of invasion: Bonaparte had amassed a sizeable army waiting for the right opportunity to invade. It never came, largely thanks to the Royal Navy (hoorah!)