Your (debug) logging messages are getting suppressed by Flask as you’re not running in debug mode. If you set the following flag to True, your code will work.
app.run(debug=True)
The messages will now appear as expected.
BennyE$ python3 stackoverflow.py
2015-03-08 12:04:04,650 ERROR: firs test message... [in stackoverflow.py:31]
* Running on http://0.0.0.0:5000/ (Press CTRL+C to quit)
* Restarting with stat
2015-03-08 12:04:04,807 ERROR: firs test message... [in stackoverflow.py:31]
--------------------------------------------------------------------------------
DEBUG in stackoverflow [stackoverflow.py:11]:
second test message...
--------------------------------------------------------------------------------
2015-03-08 12:04:13,789 DEBUG: second test message... [in stackoverflow.py:11]
192.168.178.23 - - [08/Mar/2015 12:04:13] "GET / HTTP/1.1" 200 -
--------------------------------------------------------------------------------
DEBUG in stackoverflow [stackoverflow.py:11]:
second test message...
--------------------------------------------------------------------------------
2015-03-08 12:04:14,899 DEBUG: second test message... [in stackoverflow.py:11]
192.168.178.23 - - [08/Mar/2015 12:04:14] "GET / HTTP/1.1" 200 -
This is the output in the associated output file:
BennyE$ cat output.log
2015-03-08 11:58:22,226 ERROR: firs test message... [in stackoverflow.py:31]
2015-03-08 12:04:04,650 ERROR: firs test message... [in stackoverflow.py:31]
2015-03-08 12:04:04,807 ERROR: firs test message... [in stackoverflow.py:31]
2015-03-08 12:04:13,789 DEBUG: second test message... [in stackoverflow.py:11]
2015-03-08 12:04:14,899 DEBUG: second test message... [in stackoverflow.py:11]