They have too steep an angle to be flare or swage tools. When I worked plumbing about 50 years ago, we had a couple of swages to extend copper tubing for drains (p-trap material). They had a real gradual increase in diameter so you could hammer them into the tube and create a socket to slip another piece of tubing into and solder together.
You mentioned a set of them. What sizes are they? Your photo looks like it has part numbers stamped around the rim. Maybe if you gave them the numbers they could come up with a description. What's the bottom of the smaller one look like?
You've got my curiosity up for sure.
