"To feel it less in you back....."
This seems rather odd. You suggest it is perhaps not right to feel it in your back after kickbox. The opposite is true. The power for the punches come from the back muscles, not just from the arm alone. Just as for running, the power comes from the glutes, not from the quads and hams alone. If you stand stock still, no body movement at all, you could isolate just the arms, but your punches would seriously lack power and you would not demonstrate correct form. Look at Cathe: she shoves her body into the punch.
It is perfectly normal to feel DOMS in the lats and core and shoulder after kickbox because these are your power house. Yes, you will feel DOMS less the more kickbox you do simply because your muscles become more acclimated to the movement.
Clare