A Flanger is an effects pedal that simulates two identical signals that are mixed together, but with one signal time-delayed by a small and gradually changing amount, usually smaller than 20 milliseconds. This was originally created using two tape decks but can now be done digitally using a free and open-source program called Audacity.

Step 1: What You Will Need

You will need:

A computer capable of running Audacity (Linux, Windows, or Mac)

Audacity

Dual Tape Decks Audacity Nyquist Plug-In (dualtapedecks.ny)

Stereo Butterfly (static) Audacity Nyquist Plug-In (buttrfly.ny)

A guitar recording (can be done in Audacity)

Step 2: Installing

Make sure Audacity is installed. Download Dual Tape Decks and Stereo Butterfly (static) from http://wiki.audacityteam.org/wiki/Download_Nyquist_Plug-ins.

Extract the .zip files and make sure that the nyquist file names are in lower case (eg. buttrfly.ny NOT BUTTRFLY.NY)

Copy dualtapedecks.ny and buttrfly.ny into:
/usr/share/audacity/plug-ins/ if you use Linux
OR
C:/Program Files/Audacity/Plug-Ins if you use Windows

Step 3: Preparing the Track

Open Audacity and record/import something. Make sure that the track is stereo. If it is not (and therefore mono) double-click the track to select it and click Edit...Duplicate. Click on the arrow beside the upper track and click Make Stereo Track. Delete any unwanted audio by highlighting it and then press Delete .

Step 4: Dual Tape Decks

Double-click to select the recording and then click Effect...Plugins 1 to ?...Dual Tape Decks.
I recommend using these settings:

LFO Frequency == 0.1 HZ
Starting Phase == 0 degrees
Phase Difference == 180 degrees
Depth == 0.01

Click OK to apply the effect.

Step 5: Stereo Butterfly (static)

Double-click to select the audio track. Click Effect...Plugins 1 to ?...Stereo Butterfly. Set stereo width to 0.00 and then click OK.

Step 6: Dual Tape Decks (Again)

Re-apply the Dual Tape Decks effect by double-clicking the track to select it then click on Effect...Plugins 1 to ?...Dual Tape Decks. Use the same settings as you used the first time in Step 4.

Step 7: Done

Your audio recording should now have a Flanging effect. You can now export it or add another layer to it. Have fun with this effect!

I have attached samples of this effect in MP3 and OGG formats. The OGG version will play directly in Firefox.