Back in school we were taught that all things when are illuminated create shadows, except but the flame.
Indeed the flame has not shadow, and here is an explanation of why is this so.
The shadow is creating on a given surface like wall or floor, when between the substrate and the light source interfere with an object that blocks certain part of the light beam.
However when the object itself is a source of light, like in this case with the flame, then the there is no shadow on the given surface. This is the main reason why there is no shadow of the flame on the wall.
When something becomes very hot or has burning sensation, it emits light as part of incineration process. And while the light emitted does not create a shadow, quite often material that burns it creates.
What makes it difficult to see the shadow is the fact that the flame itself sheds light from the “source” of the flame, in order to be able to see the shadow, we need a light source that is brighter (preferably sunlight) of the flame that we lit.
Try, for example, to take a candle and hold it so that sunlight falls directly on it. You should be able to see the shadow of the flame on the wall or on the floor behind the shadows.