You could do it... Might no be worth your while. Let me explain.
A flanger consists of a dry signal run in parallel with a delayed one. This would be one circuit. Then you would need a LFO and VCO to modulate (sweep) the amount of delay. Thus two more circuits. An analog (non DSP) flanger uses a delay IC (BBD) that gets controlled by a LFO/VCO combination. At the heart of the LFO is a quad op amp (LM324) that feeds into a the VCO which is a CMOS dual flip-flop IC (CD4013be).
Les Paul would get his flanging effect by recording his guitar part on a reel to reel. Then playing, real time, a cloned second part (yes he was that good!). He then would have someone press on the reel, to make the delay fluctuate.
I guess you could build a tape delay with one recording head and one playback head, and split the signal to have one dry and one delay. You would then add a circuit to fluctuate (sweep) the speed of the tape. As far as adjustment controls, you would need one to balance the amount of dry volume vs delay volume and one to adjust the rate for fluctuating the speed of the tape.
If you do it, I believe you would be the first. Not sure what it would sound like... I've done plenty of projects for the shear fun of it. If you do it, best of luck.
ttfn.