In fact, this is an old school stroke that used to be popular a long time ago and is still used by some older masters swimmers.
I would not recommend anyone using this in a competition, however, it has its benefits for learning how to do a proper butterfly stroke or breaststroke kick.
Most of all, the Butterfrog can be a great break from the every day monotonous practice.
The stroke is a combination of butterfly (also called dolphin) and breaststroke, which are both called short-axis strokes.
They both work from a pivot point in the hips and create an undulating motion forward.
The major distinction between the two strokes is the arm recovery.
Butterfly recovers above the water as you can see from the video below and breaststroke recovers right at the surface (usually at higher speeds, breaking the surface of the water).
The true butterfly uses an undulating dolphin kick and breaststroke a whip or frog kick as shown below.
Rhythm and timing basically sum up the most difficult aspect of short-axis strokes.
A good undulating motion is critical for being efficient with these two strokes.
Since the two swimming strokes are quite similar and have a lot in common, it is not as hard to combine them together, however, the resulting speed of the stroke is very slow.
For that reason, Butterfrog should not be used in competitions, even though it is still considered legal to use butterfly arms with a breaststroke kick.
Watch carefully how the legs complement the arms in this video.
And here is another video that shows you how to slow the Butterfrog down, so you can work on the technique.
How about trying it the opposite way?
Breaststroke arms and butterfly legs.
This is actually a very common breaststroke drill which teaches you a nice body undulation and lets you strengthen your arms, especially if performed with paddles.
See the video below on how to do the Breastfly drill:
In summary, if you do struggle with butterfly. The Butterfrog stroke can be a great substitute to teach the correct arm motions, so give it a go.