Mix a signal with a copy of itself delayed by a few milliseconds, then move that delay. The two signals cancel at frequencies where they are out of phase, producing a series of evenly spaced notches, and sweeping the delay drags those notches through the spectrum.
Where the sound comes from
A delay of one millisecond cancels at 500 Hz and again at every odd multiple of it. That regular pattern of notches is a comb filter, and its metallic ring is the reason a flanger sounds harmonically related to the material rather than like a separate voice.
The peaks and notches move as the delay sweeps. Since the spacing is set by the delay time, the whole comb compresses and expands as it moves, which is the rising and falling whoosh.
Base delay and depth
Base delay is where the sweep starts, from 0.1 ms to 10 ms. Depth is how much is added on top of it.
Short base delays put the first notch high up and give a thin, bright effect. Longer settings move everything down and start to sound like the chorus range, where the copy reads as a separate voice.
Feedback
Feedback returns the delayed copy to the input, so it passes through the delay repeatedly. It sharpens the peaks between the notches and is what turns a gentle sweep into a jet-engine sound.
Feedback can be negative here. Inverting the recirculated signal moves the notch pattern to a different set of frequencies and hollows out the middle, which suits drums and noise-rich material. Positive feedback resonates and suits sustained sources.
At 90% either way the resonance is strong and long. It stays stable, but a loud source at that setting will need the output level checking.
Stereo phase
The stereo phase control offsets the sweep between channels, up to 180 degrees. At 90 degrees the two sides are a quarter cycle apart, so the effect crosses the image as it moves rather than pulsing in the middle.
Mix
Interference needs both signals present, so the strongest flanging is at 50%, where the delayed copy and the original are equal.
Pushing to 100% removes the original and with it most of the cancellation. That is a useful setting when the flanger is the sound rather than an effect on a source, but it is not the deeper version of what 50% does.
Example: a drum loop that needs movement
Set base delay to 0.5 ms, depth to 2 ms, rate to 0.15 Hz, feedback to -60%, and mix to 50%.
The slow rate takes about seven seconds per pass, so the sweep works across bars rather than beats, and the negative feedback keeps the loop from turning resonant while it moves.