I am a 25+ year scuba divemaster. Alas, poor fin kicking technique is very common, even among experienced scuba divers.
First of all, selection of a fin which is too flexible is better than one which is too stiff (within limits). If you sometimes use a full 7 mm (1/4 inch) wet suit and other times no wet suit, you likely need two sets of fins. Same for snorkeling/swimming versus scuba. The extra bulk of wetsuit/tanks/weights/BCD is appropriately matched with longer and stiffer fins than when skinny dipping. (I am not sure if it is proper when wearing only fins to call it skinny.)
It is nearly impossible to select the appropriate length and stiffness in a store (at least by a novice). Fins need to be test driven. One lap in a swimming pool is usually enough to determine a good match.
Fins are designed with a variety of parameters. One of the most important is their buoyancy. If thrown into the water, do they sink or float? Sinking is good for kicking technique—especially on the surface (swimming) where density helps keep the fins in the water. If you'll be at depth (scuba), non-buoyant fins are more comfortable and easier to control—unless your swim will have elements of Cirque du Soleil. However, when removing the fins, there is a definite advantage to buoyancy so that $150 fins do not immediately tumble 700+ feet to the bottom between the Galapagos Islands (darn!).
The most common fin technique inefficiency is "bicycling". The knees should not be significantly bending. This causes the fin angle to move a lot without moving through much of the water, so it provides little propulsion but a lot of wear and tear on the feet, ankles, and knees.
Efficient kicking motion comes from the hips with the knees kept stiff. If done correctly, it won't be possible to rapidly kick—and that's okay. This video shows great kicking technique. Though he "dolphins" as for a monofin, but it works well with two fins, too. Notice how he moves the fins through a great distance but hardly flexes the knees.
This video clip shows both frog kick and flutter kick (the latter I derogatorily call bicycling). Frog kick provides nice kicking variety because it uses an entirely different set of muscles. The flutter kick does have its use: the video demonstrates how it can be used to prevent kicking up clouds of silt and minimize coral reef damage when swimming near the bottom.
By using long, patient kick cycles and keeping the ankles relaxed, stress on the ankles should be minimal. If you do feel the ankles getting sore or tired, stop, relax, and then continue with gentle large motions instead of rapid tiny kicks.