The optimum position depends on many factors.
In the past, it was common practice to point the burner a little bit down compared to kiln axis, in direction of the charge.This was primarily done to compensate the tendency of the flame to go upward due to convection and entrainement by the secondary air.
Today, with modern high momentum burners, this is no longer recommended. The jet momentum being stronger, if you point the burner toward the charge, the risk is that the flame will touch the charge. The local reducing conditions would increase sulphur circulation and increase the risk of coating and blockages in the preheater. Concensus is that high momentum burners should be placed parallel to kiln axis.
Basic positions would be on kiln axis, but the burner can also be shifted sideways (still parallel to kiln axis). Some recommend to shift the burner horizontally away from the charge when using coarse waste fuel to limit the risk that coarse particles would fall into the charge. Similarly, if you use only fine, easy to burn fuel, the burner can be shifted toward the charge to improve heat exchange. As radiation is the primary heat exchange mechanism, the effect is however limited.
Concerning insertion depth, in theory, the further inside the better. This is to get away from the perturbation of the change of direction of the secondary air and to improve the precooling zone to avoid snowmen in the cooler. There is however a limit due to the length and related weight of the burner and the risk of damage by big pieces of coating falling on the burner. Usual insertion depth would be 50cm-1m inside the kiln. But many kilns operate with the burner just at the limit of the kiln (0cm). Having the burner outside the kiln is generally not recommended.
Best regards,
O. Van Cantfort