I am a finned swimming instructor. What usually I teach is that there is the need of a perfect matching of three components:
- the biomechanics of your legs (we are all built different)
- the mechanics of your fins (there are hundredths of different shapes, geometries, rigidity, length, angle of the blade, etc.)
- the kicking style
Scuba instructors only focus on the third component, ignoring almost entirely the first two, and suggest the same type of fins to everyone and for every usage.
Of course this is entirely wrong.
But dealing simultaneously with three factors is complex, so let's fix first one of the three: the kicking style.
Basically there are 4 correct kicking style and at least one dozen wrong styles, which we will not discuss here.
The correct kicking styles are:
1) finned swimming competition (or very fast snorkeling, when a shark is chasing you), done at surface parallel to the water surface. The focus is on maximum speed, and this requires invariably a monofin and dolphin kicking.
2) free diving (that is swimming vertically down to the bottom or up to the surface, obtaining the maximum efficiency, that is less oxygen consumption for a given distance travelled). Monofins are also used, but most freedivers prefer a pair of very long, very soft fins, made in carbon fiber or fiberglass.
3) recreational scuba diving in open environment, including strong currents, vertical walls, drift diving, etc. In this case the focus is on the maximum thrust you can exert if needed, so you need a large surface and proper stiffness.
4) technical diving in wrecks, caves and small passages, where there is the risk of raising silt and suspension form the bottom, and you need to move very slowly. In this case the focus is on giving you 3D directional control with precise positioning, and avoiding to push water down towards the bottom, where it could compromise visibility. This is the reign of frog kicking.
These 4 different scenarios require different equipment (hence different fins) and different kicking technique. Furthermore, every one must evaluate if his body is fit for the task, for example I am not anymore fit for task 1) since when I was 24, so I gave up using a monofin in carbon fiber and using dolphin kicking...
I must admit that also for task 2) now, at the age of almost 62, i am not fit anymore: despite using a pair of long, super-elastic fins, I barely reach a depth of 15m while freediving, which is less than half of what I was capable when young...
Most rec scuba divers are in group 3), and I am there too. In this case the typical kicking technique to be employed is NOT frog kicking, it is the so called "power kicking"; which means a front-back scissor kicking with ample movement and little flexure of the knees, hips always perfectly extended. The typical fins used for this "power kick" are of medium length: not as long as free diving fins, not as short as "tech" fins such as the Jetfin. The typical "power" fin for group 3) is something as the Mares Plana Avanti 4, or the like. Doing frog kicking with them is feasible, but inefficient and difficult. These fins are also partially flexible, not as rigid as the Jetfin, resulting in better efficiency, but limited speed (they are not so flexible and long as freediving fins).
With equipment and kicking style of type 3) you get the maximum thrust, for example the maximum capability of pulling an heavy object to the surface without using a BCD.
The OP questions instead about frog kicking, which is the typical kicking type of group 4). Here the need for speed, thrust and efficiency are of secondary importance, and you need instead to obtain a low effort (for not wasting energy in hours-long dives) and very precise control of your movement, avoiding to push water towards the bottom. Frog kicking is perfect for this. But the need for precise movements means that the fin must become something completely rigid and an unique body with your feet. The best would be to wear them bare-foot, and to use fin which really "lock" to your feet, such as the Force Fins. Adding intermediate layers, such as the feet of your dry suit, boots, and fins with a large pocket which does not fit tight over them cause some sort of "compliance", so the movement of the feet are not transmitted directly and precisely to the fins.
Furthermore, as said at the beginning, your biomechanics play here a big role: not everyone can control effectively his feet for performing advanced propulsion methods such as reverse kicking or helicopter turn. Some gym exercises can be used for increasing mobility and muscular control of hips, knees and ankles. The choice of fins here is very important for matching the biomechanical limitations of your body, in particular the angle between the fin blade and the lower surface of your feet.
In conclusion I suggest that you start deciding which type of kicking style and fins you need to use. Do you really need to use frog kicking, as you dive wreck and caves? In most cases I have seen students that will never do that, and want to "frog kick" because they have seen this technique used by tech divers, and they are fascinated by everything is "tech". But of course frog kicking when diving against the current in a river or in a channel at Maldives is barely stupid...
If your really need to frog kick, then you should revise both your equipment and your kicking style. They interact each other, and only testing different configuration you will find the one which is good for you. Doing that with the help of a finned swimming instructor, who watches your kicking and provides hints how to improve it, can also be useful.
It appears that here on SB there are not a large number of finned swimming instructors, indeed. But possibly in your town there is a finned swimming club, and you can ask to go to the swimming pool with them. Remember, however, that most finned swimming clubs are mostly interested in competitions, so they are expert only of group 1)...