To achieve a true, vintage flanging effect, one would need to acquire two working reel-to-reel playback machines with corresponding Ampex tape and figure out some way of syncing and summing the two signals -- the BBC Radiophonic Workshop is a good resource here. Then simply get someone to ride the spool-flange on one of the machines with their finger while you perform.

An easier way to go about this would be to get yourself a new Carl Martin Vintage Flange pedal. The Vintage Flange eschews magnetic tape technology for something called a "printed circuit board" which successfully emulates the "flanging" effect in a much more compact and reliable setup.

The Carl Martin Vintage Flange is encased in a die-cast aluminum housing and features four controls: Speed, Depth, Pre-Delay and Feedback. There's even an option to switch between two pre-determined speed settings with the mere click of a footswitch. This effect could previously only be achieved by getting in your car and traveling to a different studio.

The pedal weights about 1/54th of the dual-tape machine rig, and requires only nine volts (either battery or wall-wart supplied) for proper operation. It's also a lot smarter-looking than a bulky reel-to-reel-times-two setup; much less "mad audio scientist" and way more "big man dominating acoustical-physics by merely putting his foot down."