How to stream audio using FFMPEG?
There are two solutions I can visualize for this scenario:

Saving the file to a remote computer
Having a live stream broadcast so a remote computer can receive the audio

Saving the file
This is probably the easiest method.  Allow the stream to finish recording then copy it to a predetermined location on the network.  This script should fit the bill:
#!/bin/bash
#
ffmpeg -f avfoundation -i &quot;:1&quot; -t 10 audiocapture.mp3
scp audiocapture.mp3 user@host:/foo/bar/audiocapture.mp3

exit 0

The script doesn't do any error checking of any kind but, will record from the microphone, then when finished it will copy it via SCP (secure copy) to a remote computer.    To make this work, you need to set up SSH Keys to facilitate a non-interactive login.
Stream in real time
The other method, is to broadcast the audio via TCP via a point-to-point connection. Using the same input from the previous answer, we just change the output to a network stream:
$ ffmpeg -f avfoundation -i &quot;:1&quot; -t 10 -f mpegts &quot;tcp://remote_host_or_IP_:port&quot;

Where....

-f is the transport format; in this case mpegts (MPEG Transport Stream)
tcp://remote_host_or_IP_:port is the URI value of the remote computer's hostname/IP address and port number it will be listening on.

Set remote computer to &quot;listen&quot;
Using ffplay the remote computer can be set to receive the stream (I used Windows 10 for this part, but will work in macOS/Windows/BSD/Linux)
Issue the command
ffplay -i tcp://local_host_or_IP_addr:port?listen -hide_banner

Where....

-i defines the input stream
local_host_or_IP_addr:port is the IP address or hostname  and the TCP port of the computer that's listening (not the computer that's streaming).
?listen is required to put it into &quot;listen mode&quot; otherwise it will time out if the stream is not there.

Below is an example done in Windows 10 receiving the stream from a macOS host's microphone.  The IP address of the Windows 10 machine is 10.0.0.123 and I am broadcasting on port 1234.
C:\Users\allan\Desktop\ffmpeg&gt;ffplay -i tcp://10.0.0.123:1234?listen -hide_banner

    nan    :  0.000 fd=   0 aq=    0KB vq=    0KB sq=    0B f=0/0

Once it begins to receive the broadcast, the values above will change and a player &quot;visualization&quot;  window will open up.
Input #0, mpegts, from 'tcp://10.0.0.123:1234?listen':B f=0/0
384 kb/s    nan    :  0.000 fd=   0 aq=    0KB vq=    0KB sq=    0B f=0/0
  Program 1   0.000 fd=   0 aq=    0KB vq=    0KB sq=    0B f=0/0
    Metadata: 0.000 fd=   0 aq=    0KB vq=    0KB sq=    0B f=0/0
Service01    nan    :  0.000 fd=   0 aq=    0KB vq=    0KB sq=    0B f=0/0       0B f=0/0
FFmpeg    nan    :  0.000 fd=   0 aq=    0KB vq=    0KB sq=    0B f=0/0   sq=    0B f=0/0
    Stream #0:0[0x100]: Audio: mp2 ([3][0][0][0] / 0x0003), 44100 Hz, stereo, fltp, 384 kb/s
  11.35 M-A:  0.000 fd=   0 aq=    0KB vq=    0KB sq=    0B f=0/0

It will continue to &quot;listen&quot; until the process is killed.