A flame has a shape
What holds the boundary of a flame where it is.
A flame has a shape because the balance of forces holding it in place, hot gas rising by buoyancy, fresh fuel and oxygen diffusing in from below and around, and heat escaping outward, settles into a stable pattern in space, and that pattern is what a person actually sees when they look at a flame.
Faraday's The Chemical History of a Candle is a set of lectures given to a general audience in 1861, and it goes further into the mechanics of an ordinary candle flame than most modern accounts bother to, treating the household object as worth genuinely serious attention.
A flame is made of passing gas
No single molecule of gas sits still inside a burning flame for any length of time. Fuel vapour rises from the wick or the jet, meets oxygen at a boundary, reacts, and the hot combustion products immediately rise further and are swept away, replaced by fresh fuel and fresh air arriving to take their place. What looks like an object is a steady pattern maintained by new material passing through the same region of space, in and combusted and out, fast enough that the eye reads the whole moving process as a single, stable shape.
That shape holds its outline because the forces producing it, buoyancy carrying hot gas upward, diffusion carrying fuel and oxygen toward each other, heat loss to the surrounding air, stay fairly constant under steady conditions. Change any of those inputs, blow air across the flame, tilt the candle, change the fuel supply rate, and the shape changes with them, because what has been disturbed is the balance. A flame settles into its shape within a fraction of a second of being lit and can then hold it, barely changing, for hours in still air, simply because the flows behind it settle that quickly and stay that steady.
Why a garden fountain keeps its outline
A garden fountain holds a recognisable, steady shape, a smooth arc or a rounded dome of water, even though the water making up that shape is different water at every instant, pumped up from below and immediately falling away. Nobody looking at a fountain mistakes its shape for a lump of water sitting still in the air. The shape is obviously a pattern, held in place by the balance between the pump pushing water up and gravity pulling it back down.
A candle flame is a fountain of combustion, its shape held by the same kind of balance, with fuel and heat rising and being replaced from below. Turn the fountain's pump off and the shape collapses at once, although every drop of water is still there. Starve a candle of fuel and the flame collapses the same way, vanishing the moment the flow feeding it stops, well before the surrounding air has cooled by any meaningful amount.
A gust of wind bends a fountain's arc sideways, and the arc springs back as soon as the gust passes, because the water arriving afterwards follows the old path again. A draught across a candle leans the flame over and lets it stand up again in exactly the same way, and a flame that flickers in a room with a door open is a fountain in a changing wind, each new parcel of gas following whatever the balance happens to be at that instant.
The pointed tip comes from gravity
A candle flame tapers to a point at the top because buoyancy accelerates the rising hot gas as it climbs, and a given volume of gas moving faster occupies a narrower column than the same volume moving slowly. The plume narrows the further it rises, exactly as a stream of water from a tap narrows as it falls and speeds up on its way to the plughole. The tip is the visible signature of gas accelerating upward under its own buoyancy.
Take buoyancy away entirely, as happens in orbit where hot gas has nothing to rise against, and the shape changes completely. With no upward acceleration pulling the plume into a column, fuel and oxygen have to reach each other by diffusion alone, and the flame settles into a small, roughly spherical, dim blue ball. The pointed candle shape belongs to the balance of forces acting on the flame in ordinary gravity, and a different balance produces a different shape from the same wax.
Reading a flame by its outline
Seeing a flame as a steady pattern explains why disturbing the airflow around it, even gently, changes its shape immediately and reversibly, and why a flame can be reshaped by changing the burner's geometry, the fuel supply, or the surrounding draft without touching the fuel itself. Any burner design that changes how a flame looks is, underneath, changing the balance the fuel is maintaining.
It is also why an experienced operator can read a great deal from shape alone. A flame that has gone ragged, split, or shorter than usual is reporting a change somewhere in the balance behind it, in fuel supply, in air entrainment, or in the surrounding draft, well before any thermometer or gas gauge would show the same change directly.