I wouldn't worry too much about it, how much washing is a Christmas stocking going to get? And likewise, unless the kids are smokers it wouldn't be anything I would worry about. But, LOL at burn tests. I do them all the time since I buy most of my fabrics at the thrift store. Some things are pretty spectacular when they are melting and how fast they go...
A lot of it would depend on the stocking itself. Obviously a quality product deserves a quality lining.
A number of years ago I decided I would make beautiful stockings for each member of the family. I started working away on them. And then I realized that my family wasn't going to understand or realize the awesomeness of my workmanship and that I could buy equally pretty and possibly much more detailed than I would do, close to as well made, for less than I could buy materials if I waited for the after-Christmas sales. And the good thing is that I wouldn't have to care about how they were treated or if they were kept.
Maybe I'll finish one of them for my first grand child who will be born this year, my favorite is still in the sewing room, top box on the rolling unit. The stocking part is pieced of diamond shaped red and green satin with a gold bead stitched onto each intersection. I was going to make a curved white top, like a jester's cap for the cuff and finish it off with little bells on the edge of each point.
I did make a number of simple drawstring bags and we use those for presents within the family. You just find a bag the right side and make some sort of label.