I am trying to implement the equivalent circuit of the power oscillator shown in the datasheet of the LM386, using Twin T cells as shown in the attached schematic.

The pot was used to ensure I could change gain at will.

I even swapped inputs to pins 2 & 3...

No joy.

What is wrong with it?

 

If I did my calculations right you are looking for a frequency of close to 571Hz. I have several books that have information about twin-t oscillators. In two of them the resistor to ground, in your case the 6.8k in parallel with another 6.8K needs to have a variable part. This is to compensate for the slight difference on the component values. If the capacitors and the resistors were exact you would have the 180° phase shift in the network. Plus you need to switch the connections to pin 2 and 3. In other words the network needs to be connected between the output and the inverting input. The existing pot wiper needs to be connected to the non inverting input pin 3.

 

As I said, I swapped pins as well and no joy.

 

Did you make the resistors to ground variable?

 

The same cells were used in a Twin T oscillator implemented with a CA3140 and worked OK.

 

You may want to re read my first post....the part in red.

 

Like I said on the other website, the twin-T is supposed to be used as negative feedback but you have it used as positive feedback.
You are feeding the DC from the output of the LM386 to the input pin3 that is supposed to be 0VDC. When pin3 goes to a positve voltage then the output DC voltage saturates as high as it can. A saturated output cannot provide a signal.

Make it like this but add a 100uF supply bypass capacitor: