there is an absolute translation to an efficient gymnastics kip and crossfit kip. Being that a girl that cant to 5 pullups (strict) but can kip, when shown a crossfit kip was able to do 12-15 pulls before she was out of breath and stopped, not out of power.
I think the best description is gaining speed in a horizontal plane, where its cheap and easy and then redirecting it upwards.
now for the gymnastics kip you need to have your toes by your hands for 1/4 of the swing and then kick out to redirect that force of the swing up.
Training this: starting off with a knees to elbow and then extend the legs up until toes touch the bar, then slowly lower to L sit and beyond and repeat... negatives will give the power need to hold.
alternate movement: hold L sit while swinging on the bar, this can be done on parallel bars as well, try to maintain the l sit as you swing, or even full pike.