The Axial Twist:
Kick propulsively while rotated at about 40⁰ to 60⁰, keeping both hands at thighs, while breathing continuously. The goal is to keep the kicking feet and upper butt cheek at the surface with one goggle lens UW. Fins work great, without them it's difficult sprint kicking.
Breakout drill ( https://www.youtube.com/watch?v=8mtGpRiak8c ):
Push off to 3 or 4 dolphin kicks, transition to flutter kick (without pause) taking only one powerful stroke while holding a solid flutter kick with leading arm stuck to ear in streamline (for about 6 flutter kicks), complete cycle by taking next stroke and hold again. This drill reinforces stremline at breakout to fix common mistake of opening up.
Head-up freestyle with fly kick:
I use snorkel and fins. The aft end does its action naturally, but it's a vigorous game of catch - pull - catch - pull game for the upper body. Rarely do these without the above equipment except during those high spirited swimming occasions.
The Anti-catch up:
Wear snorkel and use fins to get moving at a sufficient speed with arms back (hands at thighs). Rotate and recover up arm (but keep other hand still at thigh) counter rotate and catch following through with a pull but keep hands at thighs at end of stroke kicking several times, still rotated, ready for next arm. This drill helps me connect the (potential to kinetic) energy transfer with rotation to catch transition, as well as pulling the hand in a proper path.
Recovery (fins and, usually, a snorkel):
With down arm at side (hand at thigh), kick rotated and take half a length (12.5 or 25m) to slowly recover upper arm just to when the finger tips contact the water, and use the appropriate angles of rotation relative to arm position. Instead of entering hand, reverse the same moves for the remaining length as if being rewinded (except for direction of travel). Do it straight arm for different effect. Haven't tried this without fins, not sure if I can.