When keychain starts a new agent it does:
1259 [ -n "$pidfile_out" ] && write_pidfile && eval "$pidfile_out" > /dev/null

But the pidfile_out created by ssh-agent is dependant on the user shell and contains things like "setenv" when it's a csh-derivative, which /bin/sh dislikes. Maybe a -s in the agent invocation would help?

The symptom:

• keychain 2.9.6 ~ https://github.com/danielrobbins/keychain
• Starting ssh-agent...
  /bin/keychain: line 1259: setenv: command not found
  /bin/keychain: line 1260: setenv: command not found
• Adding 1 ssh key(s): /home/galibert/.ssh/id_rsa
• Warning: ssh-add failed: (return code: 2; output: Could not open a connection to your authentication agent.)
• Error: Unable to add keys

When trying again (with the agent running then) it works.