I have a very old Pyrex glass coffee pot that belonged to my grandmother. As a kid, I have a distant memory of her using it on a gas stove to boil water. The pot has a picture of a flame on the bottom of it, but it doesn't say either way whether it's safe to use on a gas stove. I'm sure the pot is very old; maybe 1950s or 60s. Any advice?
Sounds like what you have is Pyrex Flameware, which is range safe.
From the link:
Flameware by Pyrex by Corning Glass Works of Corning, New York is a line of range top kitchenware...
Identification of Flameware is easy as most pieces were imprinted in the bottom of each piece with the "flame" logo, plus the item number and size.
I have two Pyrex coffee pots that sound like they are the same as this. If they are Flameware, they are made for use on a stove top. I love mine.