Usually this is the TC draining back. Put it in neutral for a minute or so before taking off. Do you mean it does or doesn't do do this after sitting for a while?When I take off from a dead stop the truck will not go for a few seconds then finally kicks in and goes.
It makes a huge difference when this happens and whether it is in gear or park. Clarify a bit better.
This could be ujoints, center support bearing on rear DS (if you have one), transmisison problems, t-case, or injectors. Not enough info to even guess start checking things in the drive train.There is also quite a bit of driveline vibration going on that may or may not be related.