Out of the entire extended flute family, you've managed to name three that are about as far apart as they get! However, I'd still say that all woodwind fingerings are more similar than not.
The fife is among the oldest flutes that still get some use, and the fingerings are identical to the tin whistle (a.k.a. pennywhistle, Irish whistle). It has six holes operated by three fingers of each hand. All closed plays a low D, and picking one up at a time from the bottom results in a D major scale. The tone holes are mostly very large, meaning cross fingerings don't work very well in most cases, so most of the "in between" notes have to be done with half-holing, which is sloppy and awkward.
It's a little strange for an instrument to play in D major most naturally, so the history of woodwind fingering evolution can be thought of as a series of improvements to twist that fingering pattern into C major. In order to do that, we need to make F-natural and C-natural easy.
The recorder is the first step in that evolution, and it takes steps towards normalizing C major by extending the instrument to low C (operated by the pinky of the bottom hand--we now always play with the left hand on top, but originally either way was common), and by shrinking the tone holes so that cross fingerings work. But you still get a D major scale with the six main fingers, it's just that F and C are much easier to play. Oboe fingerings evolved alongside the recorder, and so that's the instrument with the most similar fingerings.
The thing that sets the modern flute apart is the Boehm system, which improved on many aspects, but relevant to this discussion, it introduced the automatic F# pad. It's an extra tone hole between the two hands, which plays F# and is automatically closed when any right hand key is pressed, so the old F# fingering becomes an F fingering (and F# is played by leaving the F key open, but closing a lower finger so that the F# hole closes, which is easy). The saxophone and modern clarinet have also adopted this. These instruments, plus the oboe, have also eliminated all cross fingerings and half-holing by giving each chromatic note its own tone hole, operated either by pinky keys or other automatic mechanisms.
So in all, you have (for the instruments you asked about):
C: 1 2 3 | 4 5 6 (pinky) - except fife
C#: 1 2 3 | 4 5 6 (pinky) - except fife
D: 1 2 3 | 4 5 6
D#: 1 2 3 | 4 5 6 (pinky) - flute only
E: 1 2 3 | 4 5
F: 1 2 3 | 4 - on flute
F#: 1 2 3 | 4 - on recorder, fife
G: 1 2 3
G#: 1 2 3 (pinky) - flute only
A: 1 2
Bb is a whole 'nother can of worms, as is what happens above B.