To build on Diver0001's post, a flutter kick is most useful when a constant power stroke is needed ... such as when swimming into a current. A frog kick is most useful in just about every other situation.
A frog kick is what they call a "sculling" kick ... meaning that you kick once, glide ... kick once, glide. It's a very efficient and relaxing way to dive ... but if the current's strong enough, you won't get much glide out of it.
For more power in a sculling kick, I use a variant of the scissors kick ... kind of a cross between a frog and flutter where I move my feet apart (one up, one down) and bring them back together without actually crossing them over. It's not something I learned in a course ... I just developed the kick over time because it works well in current but still provides the advantages of a sculling kick.
What's important to keep in mind is that with any of these kicks you will lose efficiency if you overkick. Most OW classes teach their students to flutter using the entire leg (from the hips down) in the kick. That method provides power, but it also leaves a whirling trail of silt behind you. For the flutter, a more effective method is to use less leg and more ankle in your kick ... think "floppy ankles". Keeping the knees bent slightly upward also helps direct water movement back behind you instead of downward ... which has the advantages of both increasing your forward momentum and kicking up less silt. That, of course, assumes that you're swimming in a horizontal plane, as you should be doing. Also remember that as you dive (again, assuming a horizontal positon) you move within a "slipstream" of disturbed water around your body. Try to keep your fins within this slipstream ... the more you do so the more effective your kick will be. You can accomplish this by using small kicks rather than large ones ... again, think floppy ankles and less leg in your kicking movement.
To frog kick properly you should keep your knees bent ... the flat side of your fins should be horizontal and parallel to the plane of your body. How you kick depends on the type of fin you're using. A standard blade fin works best with mostly ankle movement. A split fin requires less ankle and more lower leg motion.
The one I really don't use much is the dolphin kick ... where you keep your fins together and use hip and leg movements to propel yourself thru the water. They taught me this in OW ... and I don't think I've used it in a practical manner since. It's kind've fun once in a while, but never really seemed like an efficient way to move thru the water in scuba gear.
Hope this is helpful ...
... Bob (Grateful Diver)