bitflipper
A flanger or chorus would be the easiest way to get the effect. The primary difference between the two is the length of the delays: flangers using longer feedback delays than choruses. 
 
But yes, it really can be done with double-tracking. Listen to David Gilmour's vocals. They're nearly all double-tracked, as are his guitar solos. But he's so good at it you rarely notice that they're double-tracked.
 
The Bryan Ferry tune is definitely double-tracked, maybe even triple-tracked on the BGVs.

To tell the truth I did not know Gilmour's solos were double tracked, I'm going to have to check them out again. Years since I've listened to Floyd 

The Band19
Yes, a phaser is a phaser set on stun? A flanger is a phaser set to kill... Van Halen got some interesting effects using both. 

That has reminded me, I have the Waves Enigma plugin (as part of a bundle) and after all this time I've never really bothered to check it out. It actually sounds very cool. 

First you stun them? Then you kill them... Works well in more than one situation?

bitflipper
A flanger or chorus would be the easiest way to get the effect. The primary difference between the two is the length of the delays: flangers using longer feedback delays than choruses. 

Other way found. Flangers use a shorter (modulated) delay time than chorus, plus a variable amount of feedback sending the wet signal back through the input. The pitch rise and fall comes from varying the delay time in a bucket-brigade delay circuit, same thing as an analogue delay's repeats changing pitch if you set the feedback high and alter the delay time. Flangers generally work with 5-10ms delays, chorus is typically 20ms or so.

The feedback in a flanger circuit means that blending the wet signal back into the dry creates an automatically sweeping comb filter, which gives flangers the "jet plane" sound. Flangers where you can turn the LFO off (e.g. Deluxe Electric Mistress) are comb filters, with the number of "teeth" set by the amount of feedback.

This is in the analogue world.... Some digital choruses simply clone the dry sound and pitch-shift it up and down a bit, repeat for as many metallic, icy voices as required.

And tape flanging, running two tapes side by side and alternately slowing each down by touching the flange on the spools then letting it speed up to pitch, which is how the whole thing is supposed to have originated, is something a bit different again.

Yes flangers often have their delays quite short eg 3-4ms up to 8 ms or so. Choruses 10-15-20 mS delays. Don't rule out the Leslie effect either. I have run vocals through a Leslie before and mixed it under the original vocal sound. The Doppler effect sounds a bit like a chorus to a slight extent. Less like flange. If you mix this soft it can be very subtle too.
 
I heard a rumor once that Dave Gilmour actually sings the solos first and then he learns the vocal lines and plays the same parts on guitar. That would allow for double tracking the solos too because by the time he got to tracking them he would know the solo very closely.
 
Still doesn't mean he can't pull tasty things out of the hat either. Couple of live Floyd concerts I have he takes some liberties with the solos.

Leslies are strange things. Such a simple concept in hardware yet so difficult to emulate at all convincingly.

The univibe and its' various clones/sound-alikes were the original emulation attempt of course, and are still amongst the best things for doing the job in my opinion. Way better than chorus effects attempts at a rotating speaker sound. Perhaps because the univibe "chorus" setting isn't really chorus at all but a primitive phaser with a "lumpy" LFO waveform that's blended with the dry signal. I suspect because, unlike chorus, phasing doesn't smear transients or timing slightly.

Not the same as a leslie of course, but much, much cheaper and you don't need a fork-lift truck to get them on or off stage either.

The Groove 3 'Delay Explained' video with Kenny Gioia is fantastic. It covers Chorus and Flanging including the differences between them. http://www.groove3.com/str/Delay-Explained.html
 
I recently sold my Leslie 25. It was heaven on guitar. I could get that Sound Garden 'Black Hole Sun' sound. http://www.youtube.com/watch?v=3mbBbFH9fAg Too bad it took up so much real estate.
 
Rocky

Started watching the Kenny Gioia delay course. That was one of the ones I flicked past and thought "hmm delay....don't need any lessons there!" Of course all of these Groove3 courses are excellent and give you a ton of ideas. 
 
Didn't really have much luck with the Leslie-type simulation in Amplitube. But what I have done is finally pay attention to some of the Waves modulation effects which I have as part of a bundle but have never really checked out seriously. I'm getting some really cool sounds by slapping MondoMod on a bus and mixing it in with the dry vocal. Enigma is very interesting too. This is just what I was looking for. The autopanning in MondoMod is getting me close to that Chrissie Hynde sound!