Actually, it is possible to see the "settings" of a flame. You have to open the custom folder of a player (it'll be named after their username) inside of the toribash main directory, custom subdirectory, and look at the item.dat file. In there there will be lines with the FLAME0-FLAME5 heading. Those numbers after that are the unique settings that come together to create the flame, they correspond with the settings in the flame forge.
However, be aware that taking others' flame specs is a form of theft, and can go badly if you remake their flame from the exact same mold