An easy way to do this is by printing to stderr. You can do that like this:
from __future__ import print_function # In python 2.7
import sys
@app.route('/button/')
def button_clicked():
print('Hello world!', file=sys.stderr)
return redirect("https://stackoverflow.com/")
Flask will display things printed to stderr in the console. For other ways of printing to stderr, see this stackoverflow post