According to R.I.T.H. it wouldn't always be double tracked, it'd be the same take but out of phase with itself, shifting it a few milli-seconds. To do this they'd have to bounce it to another tape machine, put that tape out of alligment, and play it back on to the master over the main voice.. with all that bouncing and tape machiine being different the speed would wobble about a tiny about, thus the weirdness. The called it ADT, Automatic Double Tracking.
I think they originally called it flanging becasue it involved messing about with the flange of the tape head but they didn't realise there was already a technique/effect of the same name.