In Christian tradition, there is the Pentacost where "the holy spirit descended in tongues of flame" on the gathered disciples of Jesus.
In Jewish tradition, one writer says the Torah was "written in black fire on white fire," in discussing the eternal origins and spiritual energy of these words.
So the idea of smokeless fire being non-ordinary fire, fire of the spirit or unseen world, seems to fit with the beliefs of our religious ancestors.
However, as a person who works with fire, it bothers me to call CO2 or H20 "smoke." (I can see the spiritual sense of it, but even in ancient times smoke is not invisible - it's something you can see. I don't know if the Arabic word implies the same thing as the English word, or not.)
In English, smoke is the smudge in the air - the grey, sooty, tarry, particulate matter carried aloft from a dirty-burning fire. Most cooking fires, camp fires, torches, and cheap oil lamps produce some amount of smoke. Fire which is burned cleanly, such as a gas lantern, or a "fox stove," or a well-made and well-tended oil lamp or candle, these trim and tidy fires do not produce smoke and soot.
For a person to produce a smokeless fire, they must come to understand the world in a different way. In order to make a fire burn smokeless, you have to pay attention and give it exactly what it needs - just the right mix of fuel and air - not just "good enough" amounts of fuel and air to get what you need from it. Most cooks don't bother to make a smokeless fire; they are focused on the food, not the fire. But someone who tends a fire for its own sake, or as part of a sacred duty that allows time to study the fire, might learn this art. (Such as religious leaders tending a memorial fire or eternal flame, or night watchmen shepherding people or livestock through dangerous lands.)
Some faith traditions look at the natural world as "the big book," and consider that exploring and studying it is a way to come closer to understanding the mind of God, they call Scripture the "little book" and study both.
Perhaps in ancient times, a person who could make a smokeless fire would be understood to have a special knowledge or interaction with the unseen world.
If this is what is meant, I don't know why jinn would come only from smokeless fire, and not from wakeless boats, or perfect music, or flawless medical doctoring, or other actions showing near-perfect understanding. Maybe other acts call forth other kinds of spirits... or maybe this type of "smokeless fire," as a physical master craft, is not what is meant in the origins of jinn.
Fox stoves (partially underground, smokeless stoves dug as a tunnel out of dirt) were used on at least 5 continents going back thousands of years, including parts of the middle East and central Asia. They remain perennially popular as a stealthy way to cross enemy/rival territory without the smoke from a cooking fire giving away your location. (The "Dakota Fire Pit" is a variation that's popular on YouTube).
This might be the most common way a traveller would encounter literally smokeless fire. If this reference is literal, a traveller such as the Prophet mentioning "smokeless fire" might remind listeners of subtle scouts and desert nomads, moving unseen through vast landscapes, and making mischief or helping others at will.