"Flanging" in frequency domain? Flanging is defined as a mix of two identical signals where one signal is delayed in time by a small and gradually changing period, around 10-20 milliseconds.

Since delay in the time domain is equivalent to a phase shift in the frequency domain, could then a Flanging sound effect be done in frequency domain?

Could we do a DFT transform, make a copy of amplitudes and phases, shift phases (and gradually change the shift between -180 and +180 degrees), and add the result to original amplitudes and phases?
Frequency domain does not really work here. A flanger is NOT a linear time invariant system. You could try to implement this is "piece-wise" LTI and change the delay only at a frame boundary but this will mostly likely result in unacceptable artifacts. 

A flanger will require a time variant fractional delay. Rounding the delay the nearest integer delay results in unacceptable "zipper" noise.