Flanging is in some respects very similar to chorus in both cases, the dry signal is mixed with a delayed copy and the varying delay time is driven by an oscillator. The key difference lies in the range of delay times used. Flangers typically have a range of around 1-10ms. Because these times correspond to less than one complete waveform for most of the audible spectrum, they are low enough to introduce the interesting phenomenon of comb filtering.
When two waves are mixed together (either electronically or in the air), various types of constructive and destructive interference can occur. If the sounds are physically unrelated (for example a singer accompanying himself at the piano) we have no trouble perceiving the two as separate, because the resulting sums and differences are entirely random and therefore do not resolve into a periodic waveform. Applying a delay corresponding to more than one complete waveform usually has the same result.
At the other extreme, adding two identical waveforms together that are perfectly in phase simply results in twice the amplitude, while placing them out of phase results in perfect phase cancellation, or silence. Between these two values, complex waveforms can result, generating a set of frequency peaks or troughs corresponding to the delay time. Using an LFO to vary the delay time has the effect of sweeping these frequencies up and down in pitch. Adding flanging to a complex sound such as electric guitar results in a pleasing whooshing sound (much more pronounced than chorus) - if youve ever plugged a poorly insulated lead into a flanger, you may well have heard a sound like a faint siren as the comb filter picks defined frequencies out from the noise and sweeps them up and down.
There is a certain amount of myth surrounding the origins of this effect. Flange actually refers to the rim of an analogue tape spool. Before the development of 8, 16 or 32-track machines, engineers often used several 2 or 4-track machines synchronised together. If two machines happened to be playing identical signals (for example when using the Artificial Double Tracking technique pioneered at Abbey Road by Beatles engineer Ken Townsend), placing pressure on one reel had the effect of suddenly delaying one machine slightly, causing effects similar to modern flanging and phasing, until the synchronisation was gradually re-established. Geeks may wish to note that a sawtooth waveform therefore replicates this effect better than a sine wave! Some credit the invention of the technique to John Lennon, although this is doubtful.