Jarod,.
If you want to build one like that for fun ( to see how it works) go ahead.
If you want to build one that works well, don't build it as a cone.
The fluid dynamics of a forge chamber require a few things to operate properly.
1) The chamber must be able to heat evenly.This will require a smooth and equal wall surface without corners. - ROUND-CYLINDER. A cone would have more surface in the front than the back, creating a very uneven heating.
2) The flame must spread out as evenly as possible to heat the entire chamber equally. This is accomplished by the angle of the burner to the long axis of the chamber, and the tangent of the burner to the circumference of the chamber. The flame should be directed along the chamber wall and at a 15-20 degree angle forward. A cylinder is condusive to this. A cone would make the flame travel at a different speed as it moved forward, allowing for uneven heating.
3) Atmosphere. The fuel/air mix of the burner is only part of the atmosphere. The outside oxygen that enters into the chamber affects it,too. If you made a cone shaped chamber with a forward facing burner, you would have a venturi effect that would draw air into the rear opening.By making the cone larger at the other end you would create a nozzle effect (think rockets) drawing the air in the back even faster.
Stacy