Note that fire can have a shadow not because the incoming light beam scatters off the light in the flame. ... Fires can have shadows because they contain hot air and soot, and not because they contain light.

Can a flame ever have a shadow?

A shadow is basically the absence of light. Fire doesn't have a shadow cause fire is itself a source of light, so the wall or obstacle you'd be expecting it's shadow to fall on, would instead be covered by the light from the fire. Hence, fire has no shadow.

Which things have no shadow?

Explanation: Transparent objects doesn't form shadows. They are only formed in opaque or translucent objects.