How to connect one Android mobile audio output to the microphone of another Android mobile?
I have had a look at the Google headset specifications.
You will not be making a transcription adapter using a pile of standard Y-cables and other adapters.  That will not work.
The Android microphone input requires a certain resistance between the microphone and ground pins so that the phone can recognize the connected microphone.  Simply cobbling a bunch of plugs and cables together won't make an adapter that the phone will recognize as an external microphone.
You will have to make an adapter that the transcribing phone will recognize as an external microphone, and that reduces the electrical level of the earphone outputs to something that is appropriate for the microphone input.
Google recommends this adapter for loopback testing of Android audio circuits.

Instead of connecting the headphone input of one phone into its own microphone input, we can modify that circuit to connect the headphone output of one phone to the microphone input of a second phone.
Like this:

You will notice that I changed the value of the capacitor.  I made some measurements, and found that the circuit Google recommends attenuates the lower frequencies:

The red (earphone output) and blue (microphone input) lines should have the same shape, but with the blue line 20 dB below the red one.  The 100nF capacitor that Google specifies does terrible things to the frequency response.
The 4.7µF part in my diagram has a frequency response that looks like this:

You could build the circuit I've drawn with a 4 pole CTIA plug at both ends, then use a 4 pole Y-adapter to plug it and a headset into the phone you use for making the call.  The other end of the adapter goes to the transcription phone.
That would work, but it would be easy to plug in backwards - that wouldn't break anything, but it would be a nuisance to get properly plugged in.
Alternatively, you can build an adapter that plugs into both phones with a socket for the headset.
Finally, you can do what I did to try things out and build a headset with a transcription output.
This is the gadget I built to test the circuit:

I butchered two headsets and combined them into one unit to be certain that things will work properly before suggesting that you use my circuit.
It does work:

The same adapter could be used to transcribe phone calls or other audio from a laptop or PC - provided the laptop or PC has a 4 pole CTIA socket for the headset.  Many of them do, these days.  The signal levels should be close enough for it to work properly. I have not tested it, but it should work.
It would also be possible to make an adapter that would do transcriptions from the older, separate microphone/earphone plugs that many PCs have.

The same circuit could be used with a 3 pole socket to provide a line-in input to an Android phone for recording audio from other devices.  It will mix a stereo input to mono, and attenuate it to an appropriate level for the phone's microphone input.