Large gear teeth on slow-turning drives, crane and travel wheels, ring gears, machine slideways and ways, track surfaces, and sprockets big enough that no coil would encircle them. It is also useful where only one region of a large fabrication needs hardening and heating the whole assembly would distort it.
Like induction hardening, flame hardening produces a hard case over a core that keeps its original toughness. The depth depends on the flame, the traverse speed and the material, and it is generally deeper and less tightly controlled than an induction case. Where a drawing calls for a precise, shallow case on a part that will fit a coil, induction is the better answer.
Compare with induction hardening →
Medium-carbon and alloy steels with enough carbon to harden, typically 0.40 percent and above, and some cast irons. As with any surface hardening route, the material has to be capable of the result before the process can deliver it.

Size is far less of a constraint than with furnace or induction work, because the equipment goes to the part. Send the drawing and we will confirm.
Case depth is generally deeper and less tightly controlled. Where a part fits a coil and the drawing calls for a precise case, induction hardening is usually the better route.
Yes, and that is often the reason for choosing it. Only the surface the flame passes over is hardened.